THE REPUBLIC OF TURKEY BAHCESEHIR UNIVERSITY A FUZZY MULTI-ATTRIBUTE DECISION MAKING MODEL PROPOSAL TO SELECT CLINICAL CHIEF OF SURGERY Master’s Thesis İpek Nur AKSU ISTANBUL, 2012 THE REPUBLIC OF TURKEY BAHCESEHIR UNIVERSITY The Graduate School of Natural and Applied Sciences Industrial Engineering A FUZZY MULTI-ATTRIBUTE DECISION MAKING MODEL PROPOSAL TO SELECT CLINICAL CHIEF OF SURGERY Master’s Thesis İpek Nur AKSU Supervisor: Asst. Prof. Dr. Ahmet BEŞKESE ISTANBUL, 2012 T. C BAHÇEŞEHİR ÜNİVERSİTESİ The Graduate School of Natural and Applied Sciences Industrial Engineering Title of the Master’s Thesis : A Fuzzy Multi-Attribute Decision Making Model proposal to select clinical chief of surgery Name/Last Name of the Student : İpek Nur AKSU Date of Thesis Defense : 22.06.2012 The thesis has been approved by the Graduate School of Natural and Applied Sciences. Assoc. Prof. Dr. F. Tunç Bozbura Director This is to certify that we have read this thesis and that we find it fully adequate in scope, quality and content, as a thesis for the degree of Master of Science. Examining Committee Members: Asst. Prof. Dr. Ahmet Beşkese (supervisor) : Prof. Dr. Cengiz Kahraman : Assoc. Prof. Dr. F. Tunç Bozbura : ii ACKNOWLEDGEMENTS First of all I would like to thank my thesis supervisor Assoc. Prof. Dr. F. Tunç Bozbura and Asst. Prof. Dr. Ahmet Beşkese, who have given me the opportunity to work on this thesis. I’m very grateful for their support, guidance, encouragements and invaluable help during the preparation of this thesis. Secondly, I am very grateful to Prof. Dr. Cengiz Kahraman for taking his time to me in order to share his valuable perspectives and giving answers to my questions patiently. I would also like to thank my lecturers who encouraged me during my master program, and on my master thesis. My special thanks to my friends and colleagues, especially to Çağrı Özgün and Cihan Evecen for their comments, suggestions and their endless support all through this work, also in my personal life and masters degree courses. Last but not the least; I would like to express my love Mete Aksu and gratitude to my family as my sister Buket, my dear tiny sheep, Ercü and my father and mother for their support, motivation and patience. June, 20, 2012 İpek Nur AKSU iv ÖZET CERRAHİ KLİNİK ŞEFİ SEÇİMİNDE BULANIK ÇOK NİTELİKİ KARAR VERME MODEL ÖNERİSİ İpek Nur Aksu Endüstri Mühendisliği Yüksek Lisans Programı Tez Danışmanı: Yrd.Doç. Dr. Ahmet Beşkese Haziran 2012, 107 sayfa Günümüzde her firma, bireysel ve kurumsal verimliliği ve etkinliği arttırmayı amaçlayan çalışmalarda bulunmaktadır, şirketlerin sektörel anlamda başarılı olabilmeleri için geçerli ve uygulanabilir bir performans yönetim sisteminin kurulmasını ve işletilmesini sağlamaları gerekmektedir. Rekabet koşullarının giderek arttığı bu dönemde, şirketlerin personel performanslarının değerlendirilmesi geçmişe yönelik performans seviyesini gösterirken, geleceğe yönelik potansiyel performansı belirlemede ve performans arttırma çalışmalarında yeni bir bakış açısı sağlamaktadır. Bu çalışmanın amacı sağlık personelinin özellikle cerrahların işe alım kriterlerini belirlemektir. Çalışma, ilgili iş için 3 adayı ve yıllardır sağlık sektöründe kariyer sahibi olan 2 uzman ile gerçekleştirilmiştir. Bu çalışmada, kar amacı gözetmeyen kuruluşlarda personel performans değerlendirme sistemi, performans değerlendirme kriterlerinin belirlenmesi ve bu kriterlerin kurum açısından önem derecelerinin belirlenmesi için ağırlıklandırılması yer almaktadır. Çalışma iki bölümden oluşmaktadır, birinci bölüm İstanbul’da özel hastanelerde çalışan uzmanlardan alınan bazı bilgilerle işe alım kriterlerinin belirlenmesi ve sonrasında bütün bilgilerin bir araya getirilip işe alım kriterlerinin hiyerarşik yapısını olusturmaktır. Bulanık ortamda, kriterler Analitik Hiyerarşik Süreç ile sıralanmış ve önem dereceleri belirlenmiştir. İkinci bölüm ise pozisyon için uygun adayın TOPSIS methodu ile seçilmesidir. Sonuç olarak, işe alım kriterleri, işe alım sürecini değerlendirme çeşitli methodlar kullanılarak belirlenmiştir. Bu veriler kullanılırak uygun adaya karar verilmiştir. Anahtar Kelimeler: İşe alım süreci, Seçim, Bulanık AHP, Bulanık TOPSIS. iii ABSTRACT A FUZZY MULTI-ATTRIBUTE DECISION MAKING MODEL PROPOSAL TO SELECT CLINICAL CHIEF OF SURGERY İpek Nur Aksu Industrial Engineering Master Program Supervisor: Asst. Prof. Dr. Ahmet Beşkese June 2012, 107 pages Today’s companies, perform a work which aims to enhance individual and corporate efficiency and effectiveness. Companies need to provide establish and provide valid and applicable performance management system in order to become successful on sectoral. In a competitive environment, companies’ staff performance evaluation as indicate retrospective performance level, identify prudential potential performance and provide new perspective to studies about enhance performance. The purpose of this study is to specify the recruitment criteria of medical staff especially surgeons. Research is done on a group including 3 candidates for the related job and 2 experts that have a career in health sector for many years. In this research, staff recruitment criteria, recruitment process evaluation then performance criteria and performance process evaluation of 3 workers and the ranking of importance for the corporation are involved for the non-profit organization. There are two parts in this study, first part includes identifying the criteria for selection, some information are get from the experts which working at hospitals in Istanbul then all in information are combined to build hierarchy of recruitment criteria. By using Analytical Hierarchy Process (AHP) in fuzzy environment criteria are ranked and the importance is identified. Second part includes Fuzzy TOPSIS method to select appropriate candidate for the position. As a result, according to the methods recruitment criteria and process evaluation, for the surgeons are identified. By using these parts decided to appropriate candidate. Keywords: Recruitment Process, Selection, Fuzzy AHP, Fuzzy TOPSIS. vii        CONTENTS TABLES .................................................................................................................................. ix FIGURES .................................................................................................................................. x ABBREVIATIONS ................................................................................................................. xi SYMBOLS ............................................................................................................................. xii 1. INTRODUCTION............................................................................................................. 2 2. PROBLEM DEFINITION AND REVIEW .................................................................... 3 3. DECISION THEORY....................................................................................................... 7 3.1. DECISION MAKING PROCESS ............................................................................ 7 3.2. DECISION MAKING TYPES ................................................................................ 8 3.2.1. Single Criteria Decision-Making...................................................................... 8 3.2.2. Multi-Criteria Decision Making ..................................................................... 9 3.2.2.1Weighted sum model ........................................................................ 9 3.2.2.2Weighted product model................................................................ 10 3.2.2.3.Analytic hierarchy process ........................................................... 10 3.2.2.4.Electre............................................................................................. 14 3.2.2.5.Promethee....................................................................................... 16 3.2.2.6.Topsis .............................................................................................. 20 3.2.3. Decision Making Under Certainty................................................................. 23 3.2.4. Decision Making Under Uncertainty............................................................. 23 3.2.5. Individual Decision Making .......................................................................... 23 3.2.6. Group Decision Making.................................................................................. 24 4. FUZZY LOGIC................................................................................................................ 25 4.1. FUZZY SET THEORY ........................................................................................... 25 4.2. FUZZY NUMBERS ................................................................................................. 27 4.2.1. Triangular Fuzzy Numbers ............................................................................. 27 4.2.2. Trapezoidal Fuzzy Numbers ........................................................................... 27 5. METHODOLOGY........................................................................................................... 29 viii    5.1. APPLICATION OF FAHP AND FUZZY TOPSIS METHODS TO SELECT CLINICAL CHIEF OF SURGERY ............................................................................... 29 5.1.1. Selection Problem of Clinical Chief of Surgery............................................. 31 5.1.2. Selection Criteria of Clinical Chief of Surgery.............................................. 31 5.1.3. Solution of Clinical Chief of Surgery Selection Problem By Using Fuzzy AHP ............................................................................................................................. 34 5.1.4. Appication of Fuzzy Topsis Method to The Problem ................................... 39 6. CONCLUSION................................................................................................................. 49 REFERENCES....................................................................................................................... 51 APPENDICES ........................................................................................................................ 58 APPENDIX A1 : Questionnaire..................................................................................... 61 APPENDIX A2 : Pairwise Comparisons For Decision Criteria ................................. 68 APPENDIX A3 : Pairwise Comparisons for Decision Criteria With Fuzzy Number76 APPENDIX A4 : Curriculum Vitae Of Candidates..................................................... 83 APPENDIX A5 : Assesment of Decision Makers for Candidates............................... 89 APPENDIX A6 : Assesment of Decision Makers for Candidates with Fuzzy Numbers ............................................................................................................................ 94 APPENDIX A7 : Ratings of Candidates by Decision Makers .................................... 99 APPENDIX A8 : Fuzzy Decision Matrix of Alternatives with TOPSIS .................. 102 CURRICULUM VITAE................................................................................................ 106                 ix     TABLES   Table 3.1: Pair-wise comparison scale for AHP preferences ............................................ 13 Table 3.2: Average random consistency (RI)...................................................................... 13 Table 3.3 : Comparative Performance of widely used MADM methods ......................... 21 Table 5.1: Some academic studies about personnel selection problem ........................... 30 Table 5.2 : Linguistic Scale for Weight Matrix .................................................................. 35 Table 5.3 : Fuzzy Aggregated Decision Matrix .................................................................. 37 Table 5.4 : The geometric mean of fuzzy comparison values............................................ 37 Table 5.5: Fuzzy weight matrix............................................................................................ 37 Table 5.6 : Fuzzy weights after defuzzification and normalization.................................. 38 Table 5.7 : Illustrate linguistic variables to grade alternatives......................................... 43 Table 5.8 : The ratings of the three candidates by decision makers under all criteria... 43 Table 5.9 : The fuzzy decision matrix and fuzzy weights of three alternatives ............... 44 Table 5.10 : The Fuzzy Normalized Decision Matrix ........................................................ 45 Table 5.11 : The Fuzzy Weighted Normalized Matrix ...................................................... 45 Table 5.12 : Distance from FPIS .......................................................................................... 47 Table 5.13 : Distance from FNIS.......................................................................................... 47 Table 5.14 : Computation of di*, di- and CCi and the rating order of alternatives ....... 47                       x     FIGURES   Figure 3.1 : AHP Structure ............................................................................................ 11 Figure 4.1 : Examples of triangular fuzzy numbers ................................................... 26 Figure 4.2 : Examples of trapezoidal fuzzy numbers.................................................. 26 Figure 4.3 : Examples of Gaussian fuzzy numbers ..................................................... 26 Figure 4.4 : A Trapezoidal fuzzy number, n................................................................. 28 Figure 5.1 : The Hierarchical Structure of Candidate Selection ................................ 36 Figure 5.2 : Membership function for importance weight of criteria ........................ 36 Figure 5.3 : The Hierarchical Structure of importance criteria ................................. 38 Figure 5.4 : Membership function of linguistic terms................................................. 39       x ABBREVIATIONS AHP : Analytic Hierarchy Process FAHP : Fuzzy Analytic Hierarchy Process MADM : Multi Attribute Decision Making MCDM : Multi Criteria Decision Making TFN : Triangular Fuzzy Number TOPSIS : Technique for Order Preference by Similarity to Ideal Solution ELECTRE : Elimination and Choice Translating Reality English Elimination Et Choix Traduisant la Realité CI : Consistency Index CRI : Consistency Random Index DMs : Decision Makers WSM : Weighted Sum Model WPM : Weighted Product Model FPIS : Fuzzy Positive-Ideal Solution FNIS : Fuzzy Negative-Ideal Solution A : Alternative C : Criteria PROMETHEE : Preference Ranking Organization Method for Enrichment Evaluations r : Correlation Coefficient CR : Consistency Ratio CI : Consistency Index WSM : Weighted Sum Model WPM : Weighted Product Model xi SYMBOLS WSM score of the best alternative : * scoreWSMA − The decision criteria : n The weight of importance of the thj − criterion : jw The actual value of the thi − alternative in terms of the thj − criterion : ija The eigenvalue : maxλ : The positive outranking flow : )(a+Φ The negative outranking flow : )(a−Φ The net outranking flow : )(aΦ Preferred Index : 2 1. INTRODUCTION Along with globalization, companies must continuously develop their competition skills and keep up with the alteration in order to survive and to be float. One of the most important and efficient ways to ensure competitive success, is to invest in human resources and use this resource. Employees are the most valuable asset of a company in human resources management, which has doing set of activities carried out in order to manage effectively. The aim of human resource management is maximize the contributions of employee with business, to ensure integration of the business and increase satisfaction. Human resources management; operation will be a new addition to the selection of employees for the performance evaluation of existing employees in the making, finding the differences between employees and managers and employees play an important role in drawing up of the relationship between the features that affect. Fuzzy TOPSIS methods and Fuzzy AHP are examined in most businesses suppliers, machinery, plant location, selection of software and operating system problems, has been employed as in the literature.. In this study, clinical chief of the surgical department of a hospital with the help of these two methods for the solution to the problem of election candidates were searched. This study is aim to clarify the method of Fuzzy AHP and Fuzzy TOPSIS with an application to identify selection process of clinical chief of surgery in health sector. This study consists of two parts. The first section focused on fuzzy sets to decide criteria of selection and identify the importance of criteria to ranking selection criteria. The second section includes the selection of appropriate candidate for the position of clinical chief of surgery from alternatives using Fuzzy TOPSIS method according to selection criteria and decision makers. 3 2. PROBLEM DEFINITION AND REVIEW Health sector is expected to show a good performance. Workloads make their works difficult for healthcare workers,reduces the efficiency of employees, reduces their motivation and decreases performance. As a result, the quality of service is reduced. Based on study of Liberatore and Nydick in 2008 about the analytic hierarchy process in medical and health care decision making ,in health sector, AHP method is used in some headings, such as Patient participation, Therapy/treatment, Organ transplantation, Project and technology evaluation and selection, Health care evaluation and policy Human resources are provided for decision-making in the field of personnel selection by AHP. The AHP has been applied in hospital human resource planning and in the selection of hospital laboratory personnel selection is analyzed by Kwak et al. (1997) using AHP . Based on Weingarten et al. (1997) AHP approach for the selection of 5-year general surgery residents is discussed. In that study the AHP ratings model consists of three criteria: academic performance, personal fit, and surgical appropriateness. The weights of the criteria and the scores of the candidates were obtained from the resident selection committeeAnd also, Hemaida and Kalb (2001) applied the AHP for selecting first-year family practice residents at a Midwest medical center. This study was designed to select candidate for the position of clinical chief of surgery at a private hospital in Istanbul. 3 qualified candidates are determined for this position and the election was decided among these candidates. After the first review three candidates A1, A2 and A3 remain for further evaluation. A committee of two decision- makers, D1 and D2 has been formed to conduct the interview and to select the most suitable candidate to the position. 4 Candidate selection for surgical sciences in health sector and relevant researches studied in different subjects by using same methods are introduced in this study. AHP is a common method of multi-criteria decision-making which is developed by Thomas L. Saaty (1980). AHP paired comparison process may be inadequate in dealing with situations of uncertainty and instability therefore fuzzy AHP method has been developed to solve hierarchical problems. However, for real world environmental management problems that involve many stakeholders and conflicting viewpoints, the traditional AHP method is insufficient. Buckley (1985) applies the fuzzy theory to the AHP method to avoid neglecting extreme values. There are many studies in literature about recruitment process. Borman(1980), Day and Silverman (1989), Barrick and Mount( 1991) while discussing concept of recruitment process, they emphasize to pay attention personality factors to estimate performance of employee. Recruitment process problem sometimes use for recruit a bank employee, sometimes use for recruit a top manager (CEO). Chen and Wan (1999), Kesner and Sebora (1994) and Changati and Sambharya (1987) indicate that manager’s decisions deteramine to business strategy. Many researchers studied about selection with AHP and fuzzy AHP in terms of different perspectives in literature. Kahraman, Cebeci and Ulukan (2003) for multi- criteria supplier selection, Zouggari and Benyoucef (2011) for multi-criteria group decision supplier selection, Mahmoodzadeh, Shahrabi, Pariazar, and Zaeri (2007) for project selection, Ballı and Korukoğlu (2009) for operating system selection, Güngör, Serhadlıoğlu, Kesen (2009) for personnel selection. Dursun and Karsak (2010) for a Fuzzy MCDM approach for personnel selection, Büyüközkan and Çiftçi (2012) for A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry, Gibney and Shang (2007) for Decision making in academia: A case of the dean selection process, Kabak, Burmaoğlu and Kazançoğlu (2012) for A fuzzy hybrid MCDM approach for professional selection. 5 In literature there are many studies about personnel selection problems by using AHP and Fuzzy AHP in firms in all sectors. Today’s personnel selection are getting more important for firms and also health sector especially hospitals although there is no adequate studies in literature about staff selection in health sector. Studies in TOPSIS method by using fuzzy values have started with doctoral thesis by Negi in1989, Chen and Hwang with a published book in 1992. (Dündar et al, 2007: 292). Triantaphyllou and Lin (1996) have developed Fuzzy TOPSIS method based on fuzzy arithmetic operations.In this study, fuzzy multiple criteria decision making methods as AHP, weighted sum method, weighted product and TOPSIS model also were placed on a comparison of these methods have dealt. TOPSIS method has considered expanding the fuzzy environment by Chen (2000). In this study, the rating of each alternative and each criterion weight, triangular fuzzy numbers expressed by the verbal variables were identified with the vertex to calculate the distance between two triangular fuzzy numbers proposed method. Chu (2002), has suggested Fuzzy TOPSIS method for Location of the selection of the factory, the various alternatives in a variety of benchmarks on the basis of subjective criteria and the weights of the criteria stated in the help of linguistic variables. Jahanshahloo et al. (2006), have dealt Fuzzy TOPSIS method in fuzzy decision-making with fuzzy data. Tsaur et al. (2002), have benefied from fuzzy set theory to evaluate the quality of the airways service. AHP method was used to obtain the weights of criteria and TOPSIS method was used for grading criteria to determine factors to affects service quality. Karsak (2002), has suggested MCDM based on fuzzy distance approach to evaluate alternatives of flexible manufacturing system. Yong (2006), has suggested a new Fuzzy TOPSIS approach for Location choice of the 6 factory. The proposed method includes less mixed process when compared with existing methods. Fuzzy numbers converted to the exact digits and decreased the complexity of the transaction. Because of the latest scores are in terms of absolute numbers,there is no necessity for ranking of fuzzy numbers. Chu and Lin (2003), consider fuzzy TOPSIS method for robot selection. According to Topsis method, alternatives sort by degree of proximity coefficient, at the end of the study calculation is provided for the proposed method with numerical example. Saghafian and Hejazi (2005), suggested Fuzzy TOPSIS method for fuzzy group decision making environment and the necessary calculations have dealt MATLAB 6.5 package program for the tools. Chen et al. (2006), consider the fuzzy decision making approach to handle supplier selection problem in supply chain system. Mostly in determining the appropriate supplier quantitative and qualitative factors are taken into account, in this study the ratings and weights of these factors used in determining the linguistic variables. Bottani and Rizzi (2006), presented approach is based on set theory and fuzzy TOPSIS method for determining the most appropriate third-party logistics (3PL) service providers. Tadic et al.(2010) presented a study about ELV dismantling selection by using Fuzzy AHP and TOPSIS methods. Wang and Elhag (2006), presented Fuzzy TOPSIS method based on alpha level set and nonlinear programming. Fuzzy TOPSIS method is also discussed in the relation between the fuzzy weighted average. Supciller and Capraz (2011) consider application of supplier selection based on AHP and TOPSIS methods. Zouggari and Benyoucef (2011) suggested Multi-Criteria Group Decision Supplier Selection Problem using Fuzzy Topsis based Approach. 7 3. DECISION THEORY Due to various reasons, people will have to decide at any moment about various topics. Decision is the final judgment reached by thinking about any subject. Moreover decision making is choosing appropriate alternative with their goals among the various alternatives by decision maker. Decision theory examines decision process with analytical and systematic approach. Decision analysis or numerical methods, models, algorithms, and theories can help making decision. 3.1 DECISION MAKING PROCESS People are confronted with the decision-making throughout their lives in almost every period. There are many definitions about decision, according to Öztürk, Decision- making, to choose the most suitable one of various activities according to hand and the conditions to reach a goal. Kuruüzüm and Atsan also define that, decision-making, is one of the alternative plans of action process of selecting towards the realization goals and objectives. Actions of decision-making varies to examined the scope of the subject, whether simple or complex, and in order of severity. But in essence, the common features of these actions are the decision-making; i. All decisions, requires a variety of alternatives or options to choose from. ii. Every act of decision-making is to serve its purpose and decisions are usually intended for a particular purpose. iii. Decision-making action requires the time process. Because the decision-making process is a process that took place at various times. iv. Decisions are based on future-oriented and future estimations. v. Decision-maker, consider the possibility of not realized or has to bear the risks of the targeted goals due to the uncertainty of the future. While decision making is the selection process that chooses appropriate alternatives in case of confrontation for own purpose in these alternatives, decision making process 8 includes these transactions, respectively. Tekin has studied about the decision making process and suggests that stages of decision making process are as follows; i. Awareness of the problem ii. Identification and characterization of the problem iii. Determination of alternatives iv. Evaluation of alternatives v. Determine the best alternative vi. Evaluation of the decision Stages of decision-making process are not standardized. Problems encountered in the structure of the decision, according to the size of the environment and decided to change some of these stages. 3.2 DECISION MAKING TYPES While some events are kind of uncontrollable events, some events have partial randomness. Decision making models to be used vary depending on attributes of variables and the output of options and consequences forms. Decision-making can be classified under three main subjects as respect of the number of criteria, respect of current information and respect of decision maker. Hence the decision-making models can be classified as follows; i. Single-Criteria Decision-Making ii. Multi-Criteria Decision-Making iii. Decision Making Under Certainty iv. Decision Making Under Uncertainty v. Individual Decision-Making vi. Group Decision Making 3.2.1 Single-Criteria Decision-Making Evaluation is adhering to a single criterion in decision-making process. 9 3.2.2 Multi-Criteria Decision-Making Multiple criteria decision problems often involve conflicting. Multiple criteria decision making is the process under more than one alternative that among often conflict by decision maker’s election. In MCDM, the steps of selection can be classified as follows; Primarily determined by the relevant criteria and alternatives Degrees of importance to the criteria determined Each alternative is evaluated and the alternatives are ranked according to all criteria. (Ballı 2005 p.12 ). In the literature there are different methods used for solving MCDM. Methods commonly used in applications can be listed as follows; i. Weighted Sum Model (WSM) ii. Weighted Product Model (WPM) iii. Analytic Hierarchy Process (AHP) iv. ELECTRE v. PROMETHEE vi. TOPSIS 3.2.2.1 Weighted Sum Model (WSM) Weighted sum model is one of the most widely used methods of decision-making. If there m alternatives and n criteria, best alternative satisfies that the following expression; (Fishburn, 1967; Triantaphyllou, 2000) miforwaA n j jijScoreWSM ,...,3,2,1,max 1 * == ∑ = − (3.1) 10 In this equation * scoreWSMA − is the WSM score of the best alternative, n is the decision criteria ija is the actual value of the thi − alternative in terms of the thj − criterion and jw is the weight of importance of the thj − criterion. 3.2.2.2 Weighted Product Model (WPM) Weighted product model is comparable with weighted sum model. There is a difference that in place of addition in the model there is multiplication. Each alternative is compared with the others by multiplying a number of ratios, one for each criterion. Each ratio is increased to the power equivalent to the relative weight of the related criterion. Usually, in order to compare two alternatives KA and LA , the following product (Bridgman [1922] and Miller and Starr [1969]) have to be calculated: ∏ = = n j w LjKjLK jaaAAR 1 )/()/( (3.2) Where n is the number of criteria, ija is the actual value of the thi − alternative in terms of the thj − criterion and jw is the weight of importance of the thj − criterion and jw is the weight of importance of the thj − criterion. If )/( LK AAR is greater than or equal to one, that it shows that alternative KA is more requested than LA . 3.2.2.3 Analytic Hierarchy Process (AHP) AHP is a common method of multi-criteria decision making which is developed by Thomas L. Saaty (1980). There are many studies about AHP in the literature; the reason for this is that easily understandable method by decision-makers. Vaidya and Kumar studied about Analytic Hierarchy Process and determined the steps of the process. Steps of AHP are as follows; 11 Establish the hierarchical construction. There are different levels for goal, criteria, sub- criteria and alternatives, then compare alternatives by pair-wise comparisons matrix on the basis of each criterion. Then compare each criterion in the corresponding level and set them on the numerical scale. There will be n (n-1) / 2 comparisons, where n is the number of elements with the consideration that diagonal elements are equal ‘1’ and the other elements will simply be reciprocals of the earlier comparisons. Make the calculations to find the maximum Eigen value, consistency index CI, consistency ratio CR and normalized values for each criteria and alternative. If the maximum Eigen value, CI and CR are satisfactory then decision is taken based on the normalized values; else the procedure is repeated till these values lie in a desired range. Figure 3.1: AHP Structure The simplest method for creating the structure of a decision problem is the hierarchical structure of three-digit. The main goal is located at the top of this hierarchical structure. Consists of a lower-level criterion that affects the quality of the decision. If these criteria have properties that affect the main goal, other steps may be included in the hierarchy. Alternatives are located at the bottom of the hierarchy. Goal Criteria-1 Criteria -2 Criteria -3 Criteria -n ... Alternative -1 Alternative -2 Alternative -n ... 12 In general meaning decision making is; to choose optimum from alternative group in respect of at least one goal or factor. Therefore elements of decision making problems; decision maker, factors, results, environment and priority of decision maker. A decision problem should conceivable to choose best alternative from other alternatives which effect decision problem’s goal. In AHP the first step is determine factors and its inferior factors and constitution hierarchical structure according to decision maker’s goal. (Dagdeviren M., 2007) In AHP, firstly define the goal and try to determine factors which effect selection according to goal, in this stage should use questionnaire study or idea of professionals about this subject to determine all factors which effect selection. Thereafter determine potential alternatives according to defining factors (Saaty, T.L., 1980). As mentioned in many studies, AHP steps are included in study of Al-Harbi(2001). According to Saaty, developed the following steps for applying the AHP: 1. Define the problem and determine its goal. 2. Structure the hierarchy from the top (the objectives from a decision-maker's viewpoint) through the intermediate levels (criteria on which sub-sequent levels depend) to the lowest level which usually contains the list of alternatives. 3. Construct a set of pair-wise comparison matrices (size n x n) for each of the lower levels with one matrix for each element in the level immediately above by using the relative scale measurement shown in Table 3.1. The pair-wise comparisons are done in terms of which element dominates the other. It allows to convert the qualitative judgments into numerical values, also with intangible attributes. 13 Table 3.1 : Pair-wise comparison scale for AHP preferences Numerical rating Verbal judgements of preferences 9 Extremely preferred 8 Very strongly to extremely 7 Very strongly preferred 6 Strongly to very strongly 5 Strongly preferred 4 Moderately to strongly 3 Moderately preferred 2 Equally to moderately 1 Equally preferred 4. There are n (n -1) / judgments required to develop the set of matrices in step 3. Reciprocals are automatically assigned in each pair-wise comparison. 5. Hierarchical synthesis is now used to weight the eigenvectors by the weights of the criteria and the sum is taken over all weighted eigenvector entries corresponding to those in the next lower level of the hierarchy. 6. Having made all the pair-wise comparisons, the consistency is determined by using the eigenvalue, ߣmax, to calculate the consistency index, CI as follows: 1 max − −= n n CI λ where n is the matrix size. Judgment consistency can be checked by taking the consistency ratio CR of CI with the appropriate value in Table 3.2. 14 Table 3.2: Average random consistency (RI) Size of matrix 1 2 3 4 5 6 7 8 9 10 Random consistency 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 AHP allows inconsistency, but provides a measure of the inconsistency in each set of judgments. The consistency of the judgmental matrix can be determined by a measure called the consistency ratio (CR), defined as RI CI CR = (3.3) The CR is acceptable, if it does not exceed 0.10. If it is more, the judgment matrix is inconsistent. To obtain a consistent matrix, judgments should be reviewed and improved. 7. Steps 3-6 are performed for all levels in the hierarchy. 3.2.2.4 Electre ELECTRE (ELimination Et Choix Traduisant la REalité) for the first time the method proposed by Roy then has been developed. In 1965 the new multiple criteria outranking method was presented for the first time at a conference in Italy and then the original ideas of ELECTRE methods were first published in 1966. ELECTRE I (Roy, 1968) was the first decision-aid method using the concept of outranking relation. Tzeng and Shiau have included the model and steps of ELECTRE in the research. ELECTRE I is a discrete model. The algorithm is to search for ‘kernel’ which is a non- inferior solution. The condition of the kernel is based on the assumption of intransitive ordering of alternatives and following formula: alternative i is preferred to alternative j (i > j) if and only if c (i, j) ≥ p and 15 d (i, j) ≤ q p and q are determined by the decision makers. c (i, j) and d (i, j) are defined as follows; c (i, j) = ∑ ∑∑ =∈∈ + k k jik k ik W WW kkk 2/1 kj > k (3.4) )1( )1/()1/( ),( K fjfi Maxjid kk jik kk −= <∈ (3.5) c (i, j): concord index (3.6) d (i, j): discord index (3.7) KthWk : criterion weight (3.8) kj >ki : i>j at Kth criterion (3.9) kj =ki : alternative I and j have no difference (i=j) at Kth criterion (3.10) kk ji < : i < j alternative I is inferior to alternative j at Kth criterion (3.11) −− )1/()1/( fjfi kk : the discomfort caused by going from level − )1/( f to level )1/( f of criterion K (3.12) )1(K : total range of scale. (3.13) The idea of modulating the credibility of the outranking insertion was introduced in ELECTRE II (Roy and Bertier, 1973) where two models of preferences are taken into account: the first one being relatively poor but strongly justified and the second one richer but less defensible. ELECTRE IV is a method in which no kj is introduced. This does not mean that each criterion has exactly the same 'weight'. ELECTRE IV is appropriate for cases in which we are not willing or able to introduce information on the 16 specific role (i.e. importance) devoted to each criterion in the aggregation procedure. A sequence of nested outranking relations is introduced: ,21 rSSS ⊂⊂⊂ L (3.14) Each Si is defined by referring to concordance and discordance concepts (for an exhaustive definition of these five binary relations, see Roy and Bouyssou, 1989). ELECTRE method is designed to solve problems that require selection. ELECTRE method is based on to establish outranking relations between preferred and not preferred alternatives. To establish outranking relations, concordance and discordance indexes are created. 3.2.2.5 Promethee PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) method is one of the multi-criteria decision making method developed by Brans et al (1986). Compared with other methods, concepts and applications more easily in terms of a ranking method. PROMETHEE includes the PROMETHEE I for partial ranking of the alternatives and the PROMETHEE II for complete ranking of the alternatives. Over the years, several versions of the PROMETHEE methods such as the PROMETHEE III for ranking based on interval, the PROMETHEE IV for complete or partial ranking of the alternatives when the set of viable solutions is continuous, the PROMETHEE V for problems with segmentation constraints were developed. For each criterion, the preference function translates the difference between the evaluations obtained by two alternatives into a preference degree ranging from zero to one. In order to facilitate the selection of a specific preference function, Vincke and Brans (1985) proposed six basic types: (1) usual criterion, (2) U-shape criterion, (3) V- shape criterion, (4) level criterion, (5) V-shape with indifference criterion and (6) 17 Gaussian criterion. These six types are particularly easy to define. For each criterion, the value of anindifference threshold, q; the value of a strict preference threshold, p; and the value of an intermediate value between p and q, s, has to be fixed (Brans and Mareschal, 1992). In each case, these parameters have a clear significance for the decision-maker. Stepwise procedure for PROMETHEE II as follows. Step 1. Determination of derivations based on pair-wise comparisons dj (a,b)= gj (a) - gj (b) (3.15) Where dj (a,b) denotes the difference between the evaluations of a and b on each criterion. Step 2. Application of the preference function Pj (a,b) = Fj[dj (a,b)] j=1,...,k (3.16) Where Pj (a,b)denotes the preference of alternative a with regard to alternative b on each criterion, as a function of dj (a,b). Step 3. Calculation of an overall or global preference index ∑ = =∈∀ k j jj wbaPbaAba 1 ),(),(,, π (3.17) Where π (a,b) of a over b (from 0 to 1) is defined as the weighted sum p(a,b) of for each criterion, and wj is the weight associated with jth criterion. Step 4. Calculation the outranking flows / The PROMETHEE I partial ranking ∑∑ ∈ − ∈ + −=Φ−=Φ AxAx xanandxan ),(1 1 ),( 1 1 ππ (3.18) Where )(a+Φ and )(a−Φ denote the positive outranking flow and negative outranking flow for each alternative, respectively. Step 5. Calculation of net outranking flow / The PROMETHEE II complete ranking )()()( aaa −+ Φ−Φ=Φ (3.19) Where )(aΦ denotes the net outranking flow for each alternative. 18 These steps presents stepwise procedure for implementing PROMETHEE II. The procedure is started to determine deviations based on pair-wise comparisons. It is followed by using a relevant preference function for each criterion in Step 2, calculating global preference index in Step 3, and calculating positive and negative outranking flows for each alternative and partial ranking in Step 4. The procedure is come to an end with the calculation of net outranking flow for each alternative and complete ranking. PROMETHEE method, the steps can be summarized as follows; i. For each criterion, the alternatives are compared in pairs. Preferred level is expressed by a number in the range of [0.1]. ii. By taking the weighted average of the preferences which is calculated at first step for each criterion, multi-criteria preference index is created for each alternative. The preferred index in the range of [0.1], taking into consideration of all criteria, refers to the status of preferred α alternative to the β alternative. Weight factors are determined by the decision maker. Ranking between alternatives is done by considering the following values: is the sum of indices represents the preffered status of an alternative over all alternatives. φ+ is called outflow and α indicates how superior alternative than other alternatives. is the sum of indices indicates that the levels of all the alternatives to be preferred as compared to α. φ- is called inflow and α indicates how superior alternative than other alternatives. PROMETHEE method comprises the steps of: 19 i. General criteria selection ii. Determine the relevance of superiority iii. Evaluated choices and determine the rankings between alternatives In PROMETHEE method multi-criteria decision problem is defined as follows: { }KaIafkafMax ∈)(),...,(1 (3.20) Where K is the finite set of alternatives and f i , i= 1,…, k shows the criteria of k will be maximized. criterion for f to be of real value; Assuming that should be maximized of f: K→R; for each alternative to a K, f (a) shows the result of evaluation of this alternative. The results obtained by comparing two alternatives a,b K should be the expressed comparing in terms of preferring. Preferred Function P as follows: P = K x K →(0,1) (3.21) Preference function, indicates the level of preferring alternative a to alternative b; P (a,b) = 0 indicates that there is no difference between a and b. P (a,b) ≈ 0 indicates that a is weakly preferred according to b. P (a,b) ≈ 1 indicates that a is strongly preferred according to b. P (a,b) = 1 indicates that a is absolute preferable according to b. Preferred Function is a function of the difference between these two evaluation functions; P (a, b) = P ( f (a) – f (b) ) 20 For each node in a sequence for superiority the outflow as follows: φ+(a) =           ሺ3.22ሻ         bࣕk      Outflow equals to sum of the values of the arrows that the arrows from the node a. The symmetrical inflow as follows: φ-(a) =           ሺ3.23ሻ         bࣕk Inflow measures the quality of superiority ranking for node a. The net flow is calculated as follows; φ(a) = φ+(a) - φ-(a) (3.24) 3.2.2.6 Topsis TOPSIS (technique for order performance by similarity to ideal solution) developed by Hwang and Yoon in 1981. 21 TOPSIS (technique for order performance by similarity to ideal solution) is a useful technique in dealing with multi attribute or multi-criteria decision making (MADM/MCDM) problems in the real world. The main advantage of this method is its simplicity and ability to yield an indisputable preference order. The main concept of this method is that the most preferred alternative should have the shortest distance from the positive ideal solution (PIS) and the longest distance from the negative ideal solution (NIS). PIS is the one that maximizes the benefit criteria and minimizes the cost criteria, while the NIS maximizes the cost criteria and minimizes the benefit criteria. In traditional TOPSIS, the weights of the criteria and the ratings of alternatives are known precisely and are treated as crisp numerical data. However, under many conditions crisp data are inadequate to model real-life decision problems; in addition, perfect knowledge is not easily acquired. Unquantifiable, incomplete and non- obtainable information make precise judgment impossible. Therefore, fuzzy TOPSIS has been proposed where criteria weights and alternative ratings are given by linguistic variables that are expressed by fuzzy numbers. According to Chakraborty Table 3.3 illustrates the comparative performance of widely used MADM methods with respect to their stability, mathematical calculations involved, computational time and simplicity. Table 3.3: Comparative Performance of widely used MADM methods MADM Stability Mathematical Required Simplicity Method Calculations computational Involved time TOPSIS Medium Moderate Moderate Moderately critical AHP Poor Maximum Very High Very critical ELECTRE Medium Moderate High Moderately critical PROMETHEE Medium Moderate High Moderately 22 critical In addition to making group environments more manageable, many operations in each step of TOPSIS are scrutinized so that a broad view of TOPSIS can be established. The operations within the TOPSIS process include: decision matrix normalization, distance measures, and aggregation operators. For MADM, a decision matrix is usually required prior to the beginning of the process. The decision matrix contains competitive alternatives row-wise, with their attributes’ ratings or scores column-wise. Normalization is an operation to make these scores conform to or reduced to a norm or standard. To compare the alternatives on each attribute, the normalized process is usually made column-wise, and the normalized value will be a positive value between 0 and 1. Balli and Korukoglu performed a study about TOPSIS method that TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is one of the useful Multi Attribute Decision Making techniques that is very simple and easy to implement, so that it is used when the user prefers a simpler weighting approach. On the other hand, the AHP approach provides a decision hierarchy and requires pairwise comparison among criteria. Based on Lee et al.(2001) the user needs a more detailed knowledge about the criteria in the decision hierarchy to make informed decisions in using the AHP. TOPSIS method was firstly proposed by Hwang and Yoon (1981). Based on Beniztez et al. (2007) in this technique, the best alternative would be the one that is nearest to the positive ideal solution and farthest from the negative ideal solution. The positive ideal solution is a solution that maximizes the benefit criteria and minimizes the cost criteria, whereas the negative ideal solution maximizes the cost criteria and minimizes the benefit criteria according to Wang and Elhag (2006) and Wang and Lee (2007). Based on Ertugrul and Karakasoglu (2007) in other words, the positive ideal solution is composed of all best values attainable of criteria, whereas the negative ideal solution consists of all worst values attainable of criteria. In that study, TOPSIS method is used for determining the final ranking of the operating systems. The method is calculated as follows; 23 Step 1. Decision matrix is normalized via Eq. niJj w w r J j ij ij ij ,...,3,2,1,...,3,2,1 1 2 === ∑ = (3.25) Step 2. Weighted normalized decision matrix is formed: niJjrww ijijij ,...,3,2,1,...,3,2,1,* === (3.26) Step 3. Positive ideal solution (PIS) and negative ideal solution (NIS) are determined: (3.27) Step 4. The distance of each alternative from PIS and NIS are calculated: ( ) ( ) Jivvd Jjvvd n j jiji n j jiji ,...,2,1, ,...,2,1, 1 2 1 2** =−= =−= ∑ ∑ = −− = (3.28) Step 5. The closeness coefficient of each alternative is calculated: J1,2,...,i,* =+= − − ii i i dd d CC (3.29) Step 6. By comparing CCi values,the ranking of alternatives are determined. 3.2.3 Decision Making Under Certainty In decision making under certainty, the conditions under which the options known to be realized. There is complete information to a selection of problems in this condition. Decision makers choose the best alternative that provides the highest benefit while { } { } valuesMinimumvvvA valuesMaximumvvvA n n ,,...,, ,,...,, 21 ** 2 * 1 * −−−− = = 24 knowing the possible consequences in decision making under certainty. (Zimmermann, 1991: 241 ; Ecer). 3.2.4 Decision Making Under Uncertainty Decision making under uncertainty, the most difficult and the most common decision- making situation. In decision making under uncertainty.There are less or incomplete information related to the problem. 3.2.5 Individual Decision Making Decision-making can be divided into two group as individual and group decision- making in terms of decision maker. In individual group decision making, decision is taken by one person by selecting one alternative of all decision alternatives. 3.2.6 Group Decision Making Many people participate in decision-making process, and different personal preferences take the form of a single preferred. (Harrison, 1999: 14; imrek, 2003: 132-133; Daft, 1991) There are a number of advantages of group decision making; i. Produced a large number of alternative decision ii. Decision makers’ multilateral trend can be reduced concerning some decision alternatives. iii. Facilitates the adoption of decisions. iv. Decision alternatives can be evaluated in more detail. v. Decision alternatives may be limited within the framework of shown responses. 25 vi. Participation environment is formed. Interested persons are invited to participate in decisions. vii. Conclusions can be reached that organizational benefit not individual. viii. Offers a broad perspective of the problem identification and analysis. ix. Uncertainty can be reduced about the results of the alternatives. x. Participation allows satisfaction to the group members. xi. There are a number of disadvantages of group decision making; xii. The group may react to the decision. xiii. To decide may take a long time. xiv. To achieve consensus may be difficult. xv. The grouping may be when deciding on the group members. 4. FUZZY LOGIC 4,1 FUZZY SET THEORY Exact description of many real-life situations is very difficult to do because of the high degree of uncertainty. The concept of fuzzy logic was first given by Lotfi A. Zadeh to literature in 1965. Fuzzy logic has become more important in Japan, after 1970 in the eastern world. The Japanese used this information structure and operation of the technological devices. In the Western world in those days still making use of binary logic called the logic of Aristotle. Aristotelian logic, approaches the events as yes-no, black white, 0-1 and so on such as bilateral basis. This is not the idea of the exact location of the two values are not (Sen, 2001: 10). According to study of Application of fuzzy sets in soil science by McBratney et al.(1997) in a formal definition of a fuzzy set, we presuppose that X = {x} is a finite set 26 (or space) of points, which could be elements, objects or properties; a fuzzy subset, A of X, is defined by a function, µA, in the ordered pairs: A = {X, µA (x)} for each x ࣕ X In plain language, a fuzzy subset is defined by the membership function defining the membership grades of fuzzy objects in the ordered pairs consisting of the objects and their membership grades. The relation µA (x) is therefore termed as a membership function (MF) defining the grade of membership x (the object) in A and x ࣕ X indicates that x is an object of, or is contained in X. For all A, µA (x) takes on the values between and including 0 and 1. In practice, X = {x1, x2, … , xn } and Equation is written as: A = x1, µA (x1) + x2, µA (x2) + …+xn, µA (xn), (4.1) the + is used as defined in the set theoretic sense. If µA (x) = 0, then x,µA (x) is omitted. The membership degree of the fuzzy set can be described with triangular, trapezoidal, Gaussian, sigmodial functions or different functions can be formed with (Baslıgil, H. 2005). Figure 4.1: Examples of triangular fuzzy numbers 27 Figure 4.2: Examples of trapezoidal fuzzy numbers Figure 4.3: Examples of Gaussian fuzzy numbers 4.2 FUZZY NUMBERS A fuzzy number is a convex fuzzy set, characterized by a given interval of real numbers, each with a grade of membership between 0 and 1 (Deng, H., 1999) It is possible to use 28 different fuzzy numbers according to the situation. Generally in practice triangular and trapezoidal fuzzy numbers are used (Baykal, N., & Beyan, T., 2004). 4.2.1 Triangular Fuzzy Numbers The simplest fuzzy number is the so-called triangular fuzzy number (Bardossy and Duckstein, 1995) with its characteristic Membership Fuction written as; Fig. 4.l. illustrates the MF of triangular fuzzy number. 4.2.2 Trapezoidal Fuzzy Numbers On this issue according to study of Ertugrul, I.& Gunes, M. (2007) ,in applications it is often convenient to work with trapezoidal fuzzy numbers because of their computational simplicity, and they are useful in promoting representation and information processing in a fuzzy environment. Trapezoidal fuzzy numbers can be expressed as (n1, n2, n3, n4 ). A trapezoidal fuzzy number n  is shown in Fig. 4.4. Figure 4.4: A Trapezoidal fuzzy number, n 29 Trapezoidal fuzzy numbers are a special class of fuzzy numbers, defined by four real numbers, expressed as (n1, n2, n3, n4 ). Their membership functions are described as (4.2) There are various operations on trapezoidal fuzzy numbers. But here, three important operations used in this study are illustrated. If we define, two positive trapezoidal fuzzy numbers A = (m1, m2, m3, m4 ) and B = (n1, n2, n3, n4 ) then )/,/,/,/( ),,,( ),,,( ,,,( 14233241 4321 44332211 44332211 nmnmnmnmBA kmkmkmkmkA nmnmnmnmBA nmnmnmnmBA = =⊗ ⋅⋅=⊗ ++++=⊕ ϕ (4.3) (k is a positive real number ) According to ( Li, D.F. 2006) The distance between two trapezoidal fuzzy numbers can be calculated by using Euclidean distance as: (4.4) 5. METHODOLOGY 5.1 APPLICATION OF FAHP AND FUZZY TOPSIS METHODS TO SELECT OF CLINICAL CHIEF OF SURGERY 30 Kelemenis et al (2011) mentioned about Fuzzy TOPSIS as many scholars have deal with the human resource selection problem from the decision science point of view. Tools and techniques from operational research and artificial intelligence fields have been used to cope with this specific decision problem. Fuzzy sets and numbers, expert systems, artificial neural networks and multicriteria decision analysis techniques lie among them. Based on a critical perspective of the some academic studies as shown in Table 5.1, are the main comments that constitute the cornerstone on which the proposed approach is based. Table 5.1: Some academic studies about personnel selection problem 31 32 Kelemenis et all (2011) 5.1.1 Selection Problem of Clinical Chief of Surgery A hospital uses recruitment criteria to evaluate surgeon’s convenience to the hospital structure. Selection criteria are developed to measure important aspects of the surgeons in hospitals: Knowledge, Skills and Abilities are the main criteria, Occupational Knowledge, Foreign Language Knowledge, Graduated School and Academic Publishing are the sub-criteria of Knowledge, Basic Skills, Complex Problem Solving Skills, System Skills, Experience, Number of Case, Success rate of Cases, Stabilisation and Reference are the sub-criteria of the Skills, Psychomotor Abilities, Cognitive Abilities and Managerial Competence are the sub-criteria of the Abilities. 5.1.2 Selection Criteria of Clinical Chief of Surgery Main Criteria are determined as Knowledge, Skills and Abilities. Each criteria includes sub-criteria. 33 Knowledge: i. Occupational Knowledge: Knowledge of the information and techniques needed to diagnose and treat human injuries, diseases, and deformities and includes symptoms, treatment alternatives, drug properties and interactions, preventive health-care measures. ii. Foreign Language Knowledge: Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar. iii. Graduated School: Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D. iv. Academic Publishing: Academical papers and studies about the occupation. Skills: i. Basic Skills: Developed capacities that facilitate learning or the more rapid acquisition of knowledge. To have basis required by surgery. ii. Complex Problem Solving Skills: Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions. iii. System Skills: Developed capacities used to understand, monitor, and improve socio-technical systems. iv. Experience: Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job. v. Number of Case: To have many cases during his professional life. vi. Success rate of Cases: The presence or absence of successful cases. vii. Stabilisation: Long-term work in a hospital. viii. Reference: Views of supervisors. Abilities: Psychomotor Abilities: Abilities that influence the capacity to manipulate and control objects. 34 i. Manual Dexterity: The ability to quickly move your hand, your hand together with your arm, or your two hands to grasp, manipulate, or assemble objects. ii. Finger Dexterity: The ability to make precisely coordinated movements of the fingers of one or both hands to grasp, manipulate, or assemble very small objects. Cognitive Abilities: Abilities that influence the acquisition and application of knowledge in problem solving i. Problem Sensitivity: The ability to tell when something is wrong or is likely to go wrong. It does not involve solving the problem, only recognizing there is a problem. ii. Deductive Reasoning: The ability to apply general rules to specific problems to produce answers that make sense. iii. Inductive Reasoning: The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events). iv. Oral Comprehension: The ability to listen to and understand information and ideas presented through spoken words and sentences. v. Oral Expression: The ability to communicate information and ideas in speaking so others will understand. vi. Written Comprehension: The ability to read and understand information and ideas presented in writing. vii. Selective Attention: The ability to concentrate on a task over a period of time without being distracted. Managerial Competence: Management principles involved in strategic planning, resource allocation, human resources modeling, leadership technique, production methods, and coordination of people and resources. 35 5.1.3 Solution of Clinical Chief of Surgery Selection Problem by Using Fuzzy AHP Kahraman and Cebi was studied about selection by using Fuzzy AHP according to this study; the importance of the weights are defined by decision makers directly, they obtained by pair-wise comparisons. If the assessments of the weights are in pairwise comparisons, the importance of the weights determined by AHP. The aggregated decision matrix is constructed to satisfy each decision maker in the group if there is a group decision. Therefore, to obtain the aggregation of the importance weight of each criterion and the rating of each alternative (Chen,2000) as follows; ),,,(~,~...~...~~ 1~ ),,,( ~ , ~ ... ~ ... ~~1~ 21 21 jujmjt t j K j t jjjj ijijij t ij K ij t ijijijij wwwwwwww K w cbaSSSSS K S =++++= =+++++= (5.1) where K is the number of decision makers; ijS ~ is the ratings of alternatives; jw ~ is the importance of the criterion, and I and j represent alternative i and criterion j, respectively. Then, a fuzzy decision matrix is constructed. In this study, Buckley’s FAHP is used to find the fuzzy weights since it is easy to implement. The procedure can be summarized as follows (Chen & Hwang, 1992): ~ C = 1 ...1 ...1 2 ~ 1 ~ 2 ~ 21 ~ 1 ~~ 12 L MLMM mm n n cc cc cc (5.2) Where ~ C pair-wise comparison matrix and ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ < = > = −−−−− 11111 ~ )9,9,7(,)9,7,5(,)7,5,3(,)5,3,1(,)3,1,1(, ,1, ),9,9,7(),,9,7,5(),7,5,3(),5,3,1(),3,1,1(, ji ji ji c ij (5.3) The linguistic scale is given in Table 5, for triangular fuzzy numbers. 36 Then, the fuzzy weight matrix is calculated by Buckley’s Method as follows: ,)(( ,)( 1 ~ 2 ~ 1 ~~~ /1 ~ 2 ~ 1 ~~ −++⊗= ⊗⊗⊗= nii n iniii rrrrw cccr L L (5.4) where inc ~ is the fuzzy comparison value of criterion i to criterion n, ir ~ is the geometric mean of fuzzy comparison value of criterion i to each criterion. After the importance of weight matrix is obtained, defuzzification process which converts a fuzzy number into a crisp value is utilized. At first, fuzzy numbers will be defuzzified into crisp values and then normalization procedure will be applied. For the defuzzification process, centroid method, which provides a crisp value based on the center of the gravity, is selected since it is the most commonly used method (Opricovic & Tzeng, 2004). Following equation presents both defuzzification and normalization procedure in one formula. , 1 ~ 1 ~ ~ ∑∑ == ++== n j j rurmrl n j j r r w www w w w (5.5) where the importance of rth criterion, wr, is a non-fuzzy number and n is the number of the criteria. Acccording to the method, application of the problem can be summarized as follows; Step 1: Decision makers decide the importance level of criteria by using pair-wise comparison matrix with linguistic scale as shown in Table 5.2. Kahraman, C. , Cebi ,S.,2009 use this scale from Hsieh et al. ,2004, modified form as follows; Table 5.2: Linguistic Scale for Weight Matrix Linguistic scales Scale of fuzzy number (1,1,1) Just equal (Je) (1,1,3) Equally important (Eq) (1,3,5) Weakly important (Wk) (3,5,7) Essentially important (Es) (5,7,9) Very strong important (Vs) (7,9,9) Absolutely important (Ab) The hierarchy of the problem is shown below. 37 i. As it seen in Figure 5.1, The hierarchical structure of this decision problem’s criteria and candidates are shown. Triangular fuzzy numbers which are given in Figure 5.2 is used to transform linguistic terms in to fuzzy set as seen in Figure 5.4. Figure 5.1: The Hierarchical Structure of Candidate Selection Surgical Science Candidate Selection Knowledge Skills Abilities B a sic S kills C o m p le x P ro b le m S o lvin g S kills S ys te m S kills E xp e rie n ce N u m b e r o fC a se S u cce s s ra te o f C a se s R e fe re n ce S ta b ilis a tio n P syc h o m o to r A b ilitie s C o g n itive A b ilitie s O cc u p a tio n a l K n o w le d g e F o re ig n L a n g u a g e K n o w le d g e G ra d u a te d S ch o o l A ca d e m ic P u b lish in g M a n a g e ria l C o m p e te n c e Figure 5.2: Membership function for importance weight of criteria ii. Aggregated fuzzy matrix for mail goal can be obtained as follows: 1 5 3 7 9 1 µ x 38 Table 5.3: Fuzzy Aggregated Decision Matrix Knowledge Skills Abilities Knowledge 1.00 1.00 1.00 0.12 0.17 0.26 0.17 0.26 0.57 Skills 3.87 5.92 7.94 1.00 1.00 1.00 1.00 1.00 3.00 Abilities 1.73 3.87 5.92 0.33 1.00 1.00 1.00 1.00 1.00 Step 2: Then, the fuzzy weight matrix is calculated by Buckley’s Method as follows and stated in Table 5.5. Table 5.4: The geometric mean of fuzzy comparison values i ~ r 0.27 0.35 0.53 1 ~ r 1.57 1.81 2.88 2 ~ r 0.83 1.57 1.81 3 ~ r Step 3: After the importance of weight matrix is obtained, defuzzification process which converts a fuzzy number into a crisp value is utilized. At first, fuzzy numbers will be defuzzified into crisp values and then normalization procedure will be applied. For the defuzzification process, centroid method, which provides a crisp value based on the center of the gravity, is selected since it is the most commonly used method (Opricovic & Tzeng, 2004). Following equation presents both defuzzification and normalization procedure in one formula as stated in Table 5.6. Table 5.5: Fuzzy weight matrix i ~ w 0.05 0.09 0.20 1 ~ w 0.30 0.54 1.08 2 ~ w 0.16 0.42 0.68 3 ~ w 39 Table 5.6: Fuzzy weights after defuzzification and normalization rw ~ 0.10 Knowledge 0.54 Skills 0.36 Abilities The fuzzy weight vector of the criteria obtained by Buckley formulations is presented in Table 5.5. After that defuzzification procedure is done and Table 5.6 is obtained. In Figure 5.3.,the hierarchical structure of importance of the criteria is given after the application of procedure for all criteria. Figure 5.3: The Hierarchical Structure of importance criteria Surgical Science Candidate Selection Knowledge (0.10) Skills (0.54) Abilities (0. 36) B a sic S kills (0.03) C o m p le x P ro b le m S o lvin g S kills (0.14) S yste m S kills (0.02) E xp e rie n ce (0.15) N u m b e r o fC a se (0.08) S u cce ss ra te o fC a se s (0.30) R e fe re n ce (0.07) S ta b ilisa tio n (0.19) P sych o m o to r A b ilitie s (0.33) C o g n itive A b ilitie s (0.32) O ccu p a tio n a l K n o w le d g e (0.42) F o re ig n L a n g u a g e K n o w le d g e (0.06) G ra d u a te d S ch o o l (0.40) A ca d e m ic P u b lish in g (0.12) M a n a g e ria l C o m p e te n ce (0.35) 40 Figure 5.4: Membership functions of linguistic terms. 5.1.4 Application with a FUZZY TOPSIS Method to the Problem Human judgments, often vague and may not be possible to express the numerical values.More realistic approach, linguistic values instead of numeric values may be used.In other words, the decision criteria for current problem severity levels linguistic variables can be expressed (Chen, 2000). Which is one of FMCDM Fuzzy TOPSIS, the values of both qualitative and quantitative criteria deals with the decision criteria Fuzzy TOPSIS, has a flexible structure (Chen Et al., 2005). Fuzzy TOPSIS method and the method by which to help group decision in fuzzy environments. For the solution; the decision-makers, decision criteria, and alternatives are needed Decision-makers express their thoughts related with decision criteria and alternatives verbally. Fuzzy TOPSIS method based on the decision criteria used in evaluating alternatives for decision-makers could have a different weight lies. Fuzzy TOPSIS method with the help decision-makers about the reviews of decision criteria and alternatives, changing into a triangular or trapezoidal fuzzy numbers closeness coefficient is calculated for each alternative. Alternatives are ranked using the calculated closeness coefficients. The method of valuation of alternatives to eliminate the problems posed by the subjectivity of the group decision-making and allows for more accurate decision-making. Assume that a decision group has K persons, then the importance of the criteria and the 1 5 3 7 9 1 10 V P M F M G V µ x 41 rating of alterna- tives with respect to each criterion can be calculated as [ ] [ ]Kjjjj K ijijijij www K w xxx K x ~))...((~)(~ 1~ ~))...((~)(~ 1~ 21 21 +++= +++= (5.6) Where Kijx ~ and Kjw ~ are the rating and the importance weight of the Kth decision maker. As stated above, a fuzzy multicriteria groupdecision-making problem which can be concisely expressed in matrix format as =D~ ⎥⎥ ⎥⎥ ⎦ ⎤ ⎢⎢ ⎢⎢ ⎣ ⎡ mnmm n n xxx xxx xxx ~~~ ~...~~ ~...~~ 21 22221 11211 L MLMM (5.7) where ijx ~ , ji ,∀ and jw~ , nj ,...,2,1= are linguistic variables. These linguistic variables can be described by triangular fuzzy numbers ),,(~ ijijijij cbax = and ),,(~ 321 jjjj wwww = . To avoid the complicated normalization formula used in classical TOPSIS, the linear scale transformation is used here to transform the various criteria scales into a comparable scale. Therefore, we can obtain the normalized fuzzy decision matrix denoted by R~ . R ~ = [ ] ,~ nmij r × (5.8) where B and C are the set of benefit criteria and cost criteria, respectively, and r ij = ;,,, *** Bjc c c b c a j ij j ij j ij ∈⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ (5.9) r ij= ;,,, Cj a a b a c a ij j ij j ij j ∈⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ −−− (5.10) 42 Bjifcc ijij ∈= max * ; (5.11) Cjifaa ijij ∈= − min . (5.12) The normalization method mentioned above is to preservethe property that the ranges of normalized triangular fuzzy numbers belong to [0; 1]. Considering the different importance of each criterion, we can construct the weighted normalized fuzzy decision matrix as [ ] ,,...,2,1,~~ nivV nmij == × (5.13) where ( ) .~.~~ jijij wrv = (5.14) According to the weighted normalized fuzzy decision matrix, we know that the elements jiijv ,, ~ ∀ are normalized positive triangular fuzzy numbers and their ranges belong to the closed interval [0; 1]. Then, we can define the fuzzy positive-ideal solution (FPIS, ∗A )and fuzzy negative-ideal solution (FNIS, −A ) as ),~,...~,~( ),~,...~,~( 21 ** 2 * 1 * −−−− = = n n vvvA vvvA (5.15) Where )1,1,1(~* =jv and )0,0,0(~ =−jv , j=1,2,...,n . The distance of each alternative from *A and −A can be currently calculated as ,,...,2,1),~,~( ,,...,2,1),~,~( 1 * 1 * mivvdd mivvdd j n j iji j n j iji == == − = − = ∑ ∑ (5.16) where ),( ⋅⋅d is the distance measurement between two fuzzy numbers. A closeness coefficient is defined to determine the ranking order of all alternatives once the *id and − id of each alternative ),...,2,1( miAİ = has been calculated. The closeness coefficient of each alternative is calculated as 43 .,...,2,1,* midd d CC ii i i =+= − − (5.17) Obviously, an alternative Ai is closer to the FPIS ( ∗A )and farther from FNIS( −A ) as iCC approaches to 1. Therefore, according to the closeness coefficient, we can determine the ranking order of all alternatives and select the best one from among a set of feasible alternatives. In sum, an algorithm of the multi-person multicriteria decision making with fuzzy set approach is given in the following. Step 1: Form a committee of decision-makers, then identify the evaluation criteria. Step 2: Choose the appropriate linguistic variables for the importance weight of the criteria and the linguistic ratings for alternatives with respect to criteria. Step 3: Aggregate the weight of criteria to get the aggregated fuzzy weight jw ~ of criterion jC , and pool the decision makers' opinions to get the aggregated fuzzy rating ijx ~ of alternative iA under criterion jC . Step 4: Construct the fuzzy decision matrix and the normalized fuzzy decision matrix. Step 5: Construct the weighted normalized fuzzy decision matrix. Step 6: Determine FPIS and FNIS. Step 7: Calculate the distance of each alternative from FPIS and FNIS, respectively. Step 8: Calculate the closeness coefficient of each alternative. Step 9: According to the closeness coefficient, the ranking order of all alternatives can be determined. The grades of 3 alternatives have been issued according to 15 criteria as shown in Table 5.8. By using Table 5.7. Then, the fuzzy decision matrix is formed on the basis of triangular fuzzy numbers related to criteria and alternatives. Finally, the fuzzy weights of alternatives are determined. Table 5.9 shows the result of the mentioned functions. The normalized fuzzy decision matrix is formed as shown in Table 5.10. Finally, the weighted normalized fuzzy decision matrix is formed on the basis of Table 5.10 and the related results are presented in Table 5.11. 44 Table 5.7: Illustrate linguistic variables to grade alternatives Very poor (VP) (0,0,1) Poor (P) (0,1,3) Medium poor (MP) (1,3,5) Fair (F) (3,5,7) Medium good (MG) (5,7,9) Good (G) (7,9,10) Very good (VG) (9,10,10) Table 5.8: The ratings of the three candidates by decision makers under all criteria Criteria Candidates Decision Makers D1 D2 C11 A1 (5,7,9) (3,5,7) A2 (9,10,10) (9,10,10) A3 (7,9,10) (5,7,9) C12 A1 (3,5,7) (7,9,10) A2 (7,9,10) (9,10,10) A3 (3,5,7) (3,5,7) C13 A1 (3,5,7) (5,7,9) A2 (9,10,10) (7,9,10) A3 (7,9,10) (7,9,10) C14 A1 (7,9,10) (7,9,10) A2 (9,10,10) (9,10,10) A3 (3,5,7) (1,3,5) C21 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) A3 (9,10,10) (7,9,10) C22 A1 (5,7,9) (9,10,10) A2 (7,9,10) (5,7,9) A3 (7,9,10) (7,9,10) C23 A1 (7,9,10) (7,9,10) 45 A2 (5,7,9) (7,9,10) A3 (5,7,9) (3,5,7) C24 A1 (3,5,7) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) C25 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) A3 (5,7,9) (5,7,9) C26 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (5,7,9) (5,7,9) C27 A1 (3,5,7) (9,10,10) A2 (9,10,10) (7,9,10) A3 (3,5,7) (5,7,9) C28 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) C31 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (9,10,10) (9,10,10) C32 A1 (7,9,10) (5,7,9) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) C33 A1 (7,9,10) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) Table 5.9: The fuzzy decision matrix and fuzzy weights of three alternatives C11 C12 C13 C14 C21 A1 (4.00 6.00 8.00) (5.00 7.00 8.50) (4.00 6.00 8.00) (7.00 9.00 10.00) (3.00 5.00 7.00) A2 (9.00 10.00 10.00) (8.00 9.50 10.00) (8.00 9.50 10.00) (9.00 10.00 10.00) (7.00 9.00 10.00) A3 (6.00 8.00 9.50) (3.00 5.00 7.00) (7.00 9.00 10.00) (2.00 4.00 6.00) (8.00 9.50 10.00) C22 C23 C24 C25 C26 A 1 (7.00 8.50 9.50) (7.00 9.00 10.00) (4.00 6.00 8.00) (3.00 5.00 7.00) (7.00 9.00 10.00) A 2 (6.00 8.00 9.50) (6.00 8.00 9.50) (9.00 10.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) A 3 (7.00 9.00 10.00) (4.00 6.00 8.00) (7.00 9.00 10.00) (5.00 7.00 9.00) (5.00 7.00 9.00) 46 Table 5.10: The Fuzzy Normalized Decision Matrix Table 5.11: The Fuzzy Weighted Normalized Matrix C27 C28 C31 C32 C33 A 1 (6.00 7.50 8.50) (7.00 9.00 10.00) (7.00 9.00 10.00) (6.00 8.00 9.50) (6.00 8.00 9.50) A 2 (8.00 9.50 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) (9.00 10.00 10.00) A 3 (4.00 6.00 8.00) (7.00 9.00 10.00) (9.00 10.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) C11 C12 C13 C14 C21 A 1 (0.40 0.60 0.80) (0.50 0.70 0.85) (0.40 0.60 0.80) (0.70 0.90 1.00) (0.30 0.50 0.70) A 2 (0.90 1.00 1.00) (0.80 0.95 1.00) (0.80 0.95 1.00) (0.90 1.00 1.00) (0.70 0.90 1.00) A 3 (0.60 0.80 0.95) (0.30 0.50 0.70) (0.70 0.90 1.00) (0.20 0.40 0.60) (0.80 0.95 1.00) C22 C23 C24 C25 C26 A 1 (0.70 0.85 0.95) (0.70 0.90 1.00) (0.40 0.60 0.80) (0.30 0.50 0.70) (0.70 0.90 1.00) A 2 (0.60 0.80 0.95) (0.60 0.80 0.95) (0.90 1.00 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) A 3 (0.70 0.90 1.00) (0.40 0.60 0.80) (0.70 0.90 1.00) (0.50 0.70 0.90) (0.50 0.70 0.90) C27 C28 C31 C32 C33 A 1 (0.60 0.75 0.85) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.60 0.80 0.95) (0.60 0.80 0.95) A 2 (0.80 0.95 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.90 1.00 1.00) A 3 (0.40 0.60 0.80) (0.70 0.90 1.00) (0.90 1.00 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) C11 C12 C13 C14 C21 A 1 (0,00 0,02 0,12) (0,00 0,00 0,02) (0,00 0,02 0,12) (0,00 0,01 0,05) (0,00 0,01 0,07) A 2 (0,01 0,04 0,15) (0,00 0,00 0,02) (0,01 0,03 0,15) (0,00 0,01 0,05) (0,00 0,01 0,10) A 3 (0,01 0,03 0,15) (0,00 0,00 0,02) (0,01 0,03 0,15) (0,00 0,00 0,03) (0,00 0,02 0,10) C22 C23 C24 C25 C26 A 1 (0,01 0,06 0,40) (0,00 0,01 0,07) (0,01 0,05 0,38) (0,00 0,02 0,16) (0,03 0,17 0,84) A 2 (0,01 0,06 0,40) (0,00 0,01 0,07) (0,01 0,08 0,47) (0,01 0,04 0,23) (0,03 0,17 0,84) A 3 (0,01 0,06 0,42) (0,00 0,01 0,06) (0,01 0,07 0,47) (0,00 0,03 0,21) (0,02 0,13 0,75) C27 C28 C31 C32 C33 A 1 (0,01 0,08 0,48) (0,00 0,03 0,23) (0,02 0,12 0,52) (0,01 0,09 0,52) (0,02 0,13 0,49) A 2 (0,02 0,10 0,57) (0,00 0,03 0,23) (0,02 0,12 0,52) (0,01 0,10 0,54) (0,02 0,17 0,52) A 3 (0,01 0,06 0,45) (0,00 0,03 0,23) (0,02 0,14 0,52) (0,01 0,10 0,54) (0,02 0,15 0,52) 47 After the weighted normalized fuzzy decision matrix is formed, the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are determined by: A* = [(0.15, 0.15, 0.15), (0.02, 0.02, 0.02), (0.15, 0.15, 0.15), (0.05, 0.05, 0.05), (0.10, 0.10, 0.10), (0.40, 0.40, 0.40), (0.07, 0.07, 0.07), (0.47, 0.47, 0.47), (0.23, 0.23, 0.23), (0.84, 0.84, 0.84), (0.57, 0.57, 0.57), (0.23, 0.23, 0.23), (0.52, 0.52, 0.52),(0.54 ,0.54, 0.54), (0.52, 0.52, 0.52)] A- = [(0.00, 0.00, 0.00), (0.00, 0.00, 0.00), (0.00, 0.00, 0.00),(0.00, 0.00, 0.00), (0.0, 0.00, 0.00), (0.01, 0.01, 0.01), (0.00, 0.00, 0.00), (0.01, 0.01, 0.01), (0.00, 0.00, 0.00), (0.02, 0.02, 0.02), (0.01, 0.01, 0.01), (0.00, 0.00, 0.00), (0.02, 0.02, 0.02), (0.01, 0.01, 0.01), (0.02, 0.02, 0.02)] Then, the distance of each alternative from the FPIS and FNIS with respect to each criterion is calculated by using the vertex method by: ( ) ( ) ( )[ ] 11.012.015.002.015.000.015.0 3 1 ),( 222*1 =−+−+−=AAd ( ) ( ) ( ) ( )[ ] 07.012.000.002.000.000.000.0 3 1 , 2221 =−+−+−=−AAd Here only the calculation of the distance of the first alternative to the FPIS and FNIS for the first criterion is shown, as the calculations are similar in all steps. The results of all alternatives’ distances from the FPIS and FNIS are shown in Tables 5.12 and 5.13. 48 Table 5.12: Distance from FPIS Table 5.13: Distance from FNIS Then closeness coefficients of alternatives are calculated. According to the closeness coefficient of alternatives, the ranking order of alternatives is determined.. Value of this parameters and final ranking order of alternatives are presented in Table 14. Table 5.14: Computation of di*, di- and CCi and the rating order of alternatives A1 A2 A3 Ranking Order di* 3.61 3.52 3.59 di- 2.56 2.77 2.66 CCi 0,42 0,44 0,43 A2 > A3 > A1 C11 C12 C13 C14 C21 C22 C23 C24 C25 C26 C27 C28 C31 C32 C33 A 1 0,11 0,01 0,11 0,04 0,08 0,30 0,05 0,37 0,18 0,61 0,43 0,17 0,37 0,40 0,37 A 2 0,10 0,01 0,11 0,04 0,07 0,30 0,05 0,35 0,17 0,61 0,42 0,17 0,37 0,39 0,35 A 3 0,11 0,02 0,11 0,04 0,07 0,30 0,05 0,35 0,17 0,63 0,44 0,17 0,36 0,39 0,36 C11 C12 C13 C14 C21 C22 C23 C24 C25 C26 C27 C28 C31 C32 C33 A 1 0,07 0,01 0,07 0,03 0,04 0,23 0,04 0,21 0,10 0,48 0,27 0,13 0,29 0,30 0,28 A 2 0,05 0,01 0,09 0,03 0,06 0,23 0,04 0,27 0,14 0,48 0,32 0,13 0,29 0,31 0,30 A 3 0,09 0,01 0,09 0,02 0,06 0,24 0,03 0,27 0,12 0,43 0,26 0,13 0,30 0,31 0,30 49 Alternatives sorted in descending order by looking at the values of the relative distance of the alternatives. Accordingly, the sort determined as A2 > A3 > A1 in alternatives of Clinical chief of surgery. In other words, an alternative A2 should choose in clinical director of surgical alternatives with the highest value of the relative distance. 50 6. CONCLUSION Decision-making is often seen as a difficult process in particular group decision- making, need to made choice among many alternatives based on decision criteria, decision-making getting more difficult. Such decision is appropriate to use the theory of fuzzy decision making in many environments. Thus, the uncertainty in the evaluation of the data using the fuzzy approach can be effectively represented, and a decision can be reached more effectively. In this study, selection problem in the health sector for the surgeon the FAHP method was proposed. First, the decision criteria defined as knowledge, skills and abilities by decision makers in command of the subject in business. And sub-criteria defined as Occupational Knowledge, Foreign Language Knowledge, Graduated School, Academic Publishing for knowledge, Basic Skills, Complex Problem Solving Skills, System Skills, Experience, Number of Case, Success Rate of Cases, Stabilisation, Reference for skills, Psychomotor Abilities, Cognitive Abilities, Managerial Competence for abilities. Criteria and alternatives were evaluated by pairwise comparisons in the method of FAHP. These evaluations were made with the help of questionnaires. Two decision makers in the enterprise answered questionnaire then fuzzy decision matrices were created with these values then determined priority values of selection criteria. In the application of the study, selection criteria are determined with Fuzzy AHP method then according to priority degree of criteria, appropriate candidate is chosen among three candidates to the position of clinical chief of surgery by using Fuzzy TOPSIS method. In this context, two decision makers assessed selection criteria by using questionnaire for each candidate then criteria are ordered according to their importance level. After evolution of criteria by using Fuzzy AHP, decision makers assessed each candidates according to priority of criteria to select appropriate candidate by using Fuzzy TOPSIS. 51 The closeness coefficients of candidates were evaluated by using Fuzzy TOPSIS method algorithm. The candidate with the highest coefficient of closeness, according to evaluation that the best surgeon for the position. After determining the fuzzy positive and negative ideal solution, the distances from these points of each alternative are calculated and closeness coefficient of each alternative are obtained separately. By looking at the values of closeness coefficient, ranking of alternatives was determined as A2> A3> A1. The results obtained in accordance with candidate A2 is proposed to recruit for the position of chief of the hospital's surgical clinic. 52 REFERENCES Periodicals Alecos Kelemenis , Kostas Ergazakis, Dimitrios Askounis (2011) Support managers’ selection using an extension of fuzzy TOPSIS Expert Systems with Applications 38 pp. 2774–2782. Balli,S. and Korukoglu,S.,(2009). Operating System Selection Using Fuzzy AHP and TOPSIS methods. Mathematical and Computational Applications, Vol. 14, No. 2, pp. 119-130. Ballı, S. (2005) Fuzzy Çok Kriterli Karar Verme ve Basketbolda Oyuncu Seçimine Uygulanması (Basılmamıs Yüksek Lisans Tezi), Mugla Üniversitesi FenBilimleri Enstitüsü, Mugla. Ballı, S., Korukoğlu, S., 2009. Operating System Selection Using Fuzzy AHP and TOPSIS Methods. Mathematical and Computational Aplications, 14(2), pp. 119-130. Barber A.E. ,(1998) Recruiting Employess:Individual and Organizational Perspectives,Sage,Thousand Oaks,CA. Bardossy, A., Duckstein, L., (1995). Fuzzy Rule-Based Modelling with Applications to Geophysical, Biological and Engineering Systems. CRC Press, New York, pp.113. Barrick, M., & Mount, M. (1991). The big five personality dimensions and job performance: A meta-analysis. Personnel Psychology, 44, pp. 1−26. Başlıgil, H.(2005): The Fuzzy Analytic Hierarchy Process for Software Selection Problems.Journal of Engineering and Natural Sciences. 2 pp.24-33. Baykal, N., Beyan, T.(2004): Bulanık Mantık İlke ve Temelleri. Bıçaklar Kitabevi İstanbul. Behzadian , M., Kazemzadeh , R.B. , Albadvi , A. , Aghdasi M. (2010). PROMETHEE: A comprehensive literature review on methodologies and applications European Journal of Operational Research 200, pp.198–215. Benitez, J. M., Martin, J. C., and Roman, C., (2007). Using fuzzy number for measuring quality of service in the hotel industry, Tourism Management, 28 (2), pp. 544– 555. 53 Blauw, P.W, (2002). ‘Recruitment Strategies and Labour Mobility’The Netherlands, (Windolf & Wood 1988,137) Borman, W. C., Rosse R. L., Abrahams, N. M., (1980), “An Empirical Construct Validity Approach to Studying Predictor-Job Performance Link”, Journal of Applied Psychology, 65, pp. 662-671. Bottani, E., Rizzi, A. (2006). A Fuzzy TOPSIS Methodology to Support Outsourcing of Logistics Services, Supply Chain Management: An International Journal, 11(4),p p.294-308. Bozbura,F.T., Beskese, (2007) A.‘Prioritization of organizational capital measurement indicators using fuzzy AHP’ Fuzzy Decision-Making Applications Volume 44, Issue 2,pp. 124-147 , doi:10.1016/j.ijar.2006.07.005. Brans, J.P., Mareschal, B., (1992) PROMETHEE V – MCDM problems with segmentation constraints. INFOR 30 (2), pp.85–96. Brans, J.P., Vincke, Ph., Mareschal, B., (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research 24, 228-238. Büyüközkan, G., Çiftçi, G. 2012 .A combined fuzzy AHP and fuzzy TOPSIS based Strategic Analysis of Electronic Service Quality in Healthcare Industry. Expert Systems with Applications, 39(3), pp. 2341-2354. Chaganti, R. and Sambharya R. (1987). ‘Strategic orientation and characteristics of upper management’, Strategic Management Journal, 8, pp. 393-401. Chakraborty S. ( 2011)Applications of the MOORA method for decision making in manufacturing environment. International Journal of Advanced Manufactur- ing Technology, doi:10.1007/s00170-010-2972-0. Chen, C. T. (2000). Extensions of the TOPSIS for Group Decision-Making under Fuzzy Environment, Fuzzy Sets and Systems, 114, pp.1-9. Chen, C. T., Lin, C. T., Huang, S. F. (2006). A Fuzzy Approach for Supplier Evaluation and Selection in Supply Chain Management, International Journal of Production Economics, 102, pp. 289–301. Chen, H., Wan, T., (1999), “A Conceptual Selection Framework Insider CEO Succession”, International Journal of Management, 16, pp. 422-431. Chen, S. J., & Hwang, C. L. (1992). Fuzzy multi attribute decision making: methods and applications. New York: Springer-Verlag. 54 Chu, T.C. (2002). Selecting Plant Location via Fuzzy TOPSIS Approach, The International Journal of Advanced Manufacturing Technology, 20, pp.859- 864. Chu, T.C., Lin, Y. C. (2003). A Fuzzy TOPSIS Method for Robot Selection, The International Journal of Advanced Manufacturing Technology, 21, pp.284-290. Day, D., & Silverman, S. (1989). Personality and job performance: evidence of incremental validity. Personnel Psychology, 42, pp. 25-36. Deng, H., (1999) Multicriteria Analysis with Fuzzy Pairwise Comparison. International Journal of Approximate Reasoning. 21,pp. 215-231. Doğan M. (1985). işletmelerde Karar Verme Teknikleri, Bilgehan Basımevi, izmir. Dursun, M., Karsak, E. E. 2010. A Fuzzy MCDM Approach for Personnel Selection. Expert Systems with Applications, 37(6), pp. 4324-4330. Ertugrul, I. and Karakasoglu, N., (2007). Performance evaluation of Turkish cement firms with fuzzy analytic hierarchy process and TOPSIS methods, Expert Systems with Applications, Article in Press, doi:10.1016/j.eswa.10.014. Gatewood R.D. ,Feild H.S.,Human Resource Selection,5th ed.pp. 9-10 Gibney, R., Shang, J. 2007 .A Decision making in academia: A case of the dean selection process. Mathematical and Computer Modelling, 46(7-8), pp. 1030- 1040. Goumas, M., Lygerou, V. (2000). An Extension of the PROMETHEE Method for Decision Making in Fuzzy Environment: Ranking of Alternative Energy Exploitation Projects, European Journal of Operational Research, 123, p.606-613. Güngör, Z., Serhadlıoğlu, G., Kesen, S. E. 2009. A Fuzzy AHP Approach to Personnel Selection Problem. Applied Soft Computing, pp. 641-646. Harrison, E. F., (1999), The Managerial Decision Making Process, Houghton Mifflin. Hemaida, R.S. & Kalb, E., (2001). Using the analytic hierarchy process for the selection of first-year family practice residents. Hospital Topics 79 (1), pp.11–15. Hsieh, T. Y., Lu, S. T., & Tzeng, G. T. (2004). Fuzzy MCDM approach for planning and design tenders selection in public office buildings. International Journal of Project Management, 22, pp. 573–584. Hwang C. L. and Yoon, K., (1981) Multiple attributes decision making methods and applications, Springer, Berlin. 55 Hwang, C. L., & Yoon, K. (1981). Multiple attributes decision making methods and applications. Berlin: Springer. İmrek, M. K., (2003), The Managerial Decision Making Process, Houghton Mifflin Yoneticiler İcin Karar Verme Teknikleri El Kitabı, Beta Basım,İstanbul. Jahanshahloo, G. R., Hosseinzadeh, L. F., Izadikhah, M. (2006). Extension of the TOPSIS Method for Decision Making Problems with Fuzzy Data, Applied Mathematics and Computation,181(2), pp.1544-1551. Kabak, M., Burmaoğlu, S. & Kazançoğlu, Y. 2012 . A fuzzy hybrid MCDM approach for professional selection. Expert Systems with Applications, 39(3), pp. 3516- 3525. Kahraman C., Ruan D., Dogan İ.(2003)’ Fuzzy group decision-making for facility location selection’ Volume 157, pp. 135-153,2003 doi:10.1016/S0020- 0255(03)00183-X. Kahraman, C. , Cebi ,S. (2009) A new multi-attribute decision making method: Hierarchical fuzzy axiomatic design.Expert Systems with Applications 36, pp.4848–4861. Kahraman, C., Cebeci, U. & Ulukan, Z, 2003. Multi-criteria supplier selection using fuzzy AHP. Logistics Information Management, 16(6), pp. 382-394. Kamal M. Al-Subhi Al-Harbi (2001) Application of the AHP in project management International Journal of Project Management 19, pp. 19-27. Karsak, E. E. (2002). Distance-Based Fuzzy MCDM Approach for Evaluating Flexible Manufacturing System Alternatives, International Journal of Production Research, 4013, pp.3167-3181. Kelemenis, A. ,Ergazakis, K., Askounis, D., (2011). Support managers’ selection using an extension of fuzzy TOPSIS Expert Systems with Applications 38, pp. 2774– 2782. Kesner, I.F., & Sebora, T.C. (1994). Executive succession: Past, present & Future. Journal of Management, 20, pp. 327-372. Klesges R.C., Sanchez V. C. and Stanton A. L. ,(1982). Professional Psychology. 1982 Aug Vol 13(4) pp. 577-586. Kuruüzüm, A., Atsan, N. (2001). Analitik Hiyerarsi Yöntemi ve Isletmecilik Alanındaki Uygulamaları, Akdeniz İ.İ.B.F Dergisi, Cilt:1, pp.83-105. Kwak, N.K., McCarthy, K.J., Parker, G.E., (1997). A human resource planning model for hospital/medical technologists:An analytic hierarchy process approach. Journal of Medical Systems 21 (3), pp.173–187. 56 Lazarevic, S.P., (2001)‘Personnel Selection Fuzzy Model International Transactions in Operational Research’ 8 (1), pp.89–105. doi:10.1111/1475- 3995.00008. Lee, W. B., Lau, H., Liu, Z. and Tam, S., (2001). A fuzzy analytic hierarchy process approach in modular product design, Expert Systems, 18 (1), pp. 32–42. Li, D.F (2006). Compromise Ratio Method for Fuzzy Multi-Attribute Group Decision Making. Applied Soft Computing. Article in press. Liberatore , M.,J. & Nydick, R., (2008) The analytic hierarchy process in medical and health care decision making: A literature review European Journal of Operational Research 189, pp.194–207. Mahmoodzadeh, S., Shahrabi, J., Pariazar, M.& Zaeri, M. S. (2007). Project Selection by Using Fuzzy AHP TOPSIS Technique. World Academy Science, Engineering and Technology. McBratney, A.B., Inakwu, O.A., Geoderma,O., (1997) Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions 77,pp.85-113. Murphy, C. K.,(1995) Limits on the analytic hierarchy process from its consistency index, European Journal of Operation Research, vol.65, pp.138-139. Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), pp.445–455. Öztürk A. (2004). Yöneylem Araştırması, Ekin Kitabevi, Bursa. Roy, B. and Bertier, E., (1973), 'La mrthode ELECTRE II-Une application aumrdia- planning', in OR '72, M. Ross (ed.), North-Holland Publishing Company, pp.291-302. Roy, B. and Bouyssou, D. (1989), 'Procrdures d'agrrgation multicritres non fondres surun critre unique de synthse', Universit6 de Paris-Dauphine, Document du LAMSADE Roy, B.(1968), 'Classement et choix en prrseuce de points de vue multiples (la mrthode ELECTRE)', Outranking Approach and The Foundations of Electre Methods 8, pp.57- 75. Saaty TL, Kearns KP . (1991). Analytical planning: the organization of systems. The analytic hierarchy process series;vol. 4RWS PublicationsPittsburgh, USA. 57 Saaty TL. (1980).The analytic hierarchy process. New York: McGraw- Hill. Saaty TL. (1985).Decision making for leaders. Belmont, California: Life Time Leaning Publications, Saaty TL. (1990).How to make a decision: the analytic hierarchy pro- cess. European Journal of Operational Research, North-Holland, 48, pp.9-26. Saghafian S., Hejazi S.R. (2005). Multi-criteria Group Decision Making Using A Modified Fuzzy TOPSIS Procedure” Proceedings of the 2005 International Conference on Computational Intelligence for Modeling, Control and Automation, and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC’05), IEEE Computer Society. Sen, Z., (2001). Bulanık Mantık ve Modelleme İlkeleri, Bilge Kultur Sanat, İstanbul. Supciller, A. A., Capraz, O. (2011) AHP-TOPSIS Yontemine Dayali Tedarikci Secimi Uygulamasi, Ekonometri ve Istatistik, 13, pp.1-22. Tadic, D., Arsovski, S., Stefanovic, M., Aleksic, A., (2010) A Fuzzy AHP and TOPSIS for ELV Dismantling Seletion, 4th Internationa Quality Conference pp.377-384. Tekin M. (2004). Sayısal Yöntemler, 5. Baskı, Konya. Triantaphyllou, E., Lin, C.T. (1996). Development and Evaluation of Five Fuzzy Multiattribute Decision-Making Methods, International Journal of Approximate Reasoning, 14, pp.281-310. Tsaur, S. H., Chang, T. Y., Yen, C. H. (2002). The Evaluation of Airline Service Quality by Fuzzy MCDM, Tourism Management, 23, pp.107-115. Tzeng, G.H., & Shiau,T.A., (1987). Energy conservation strategies in urban transportation: Application of multiple criteria decision-making, Energy Systems and Policy Vol.11 pp.1-19. Vaidya,O. S., Kumar S. (2006).Analytic hierarchy process: An overview of applications European Journal of Operational Research 169, pp.1–29. Vander Meeren, W. (1999), ‘Functieanalyse, werving en voorselectie’, in: F. Kluytmans (ed.), Leerboek Personeelsmanagement, Deventer/Heerlen: Kluwer/Open Universiteit, pp. 93-110. Wang Y. M. and Elhag T. M. S., (2006). Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment, Expert Systems with 58 Applications, 31, pp. 309–319. Wang, Y-J. and Lee, H-S., (2007). Generalizing TOPSIS for fuzzy multiple-criteria group decision-making, Computers & Mathematics with Applications, 53(11), pp. 1762– 1772. Wang, Y. M., Elhag, T. M. S. (2006). Fuzzy TOPSIS Method Based on Alpha Level Sets with an Application to Bridge Risk Assessment, Expert Systems with Applications, 31, pp.309-319. Windolf, P.& Wood S.(1988) , Recruitment and Selection in the Labour Market, Aldershot: Avebury. Yong, D. (2006). Plant Location Selection Based on Fuzzy TOPSIS, International Journal of Advanced Manufacturing Technology, 28, pp.839-844. Zimmermann, (1991): 241 ; Ecer,Fuzzy Set Theory and Its Applications, Kluwer Academic Publishers, London Zouggari, A., Benyoucef, L., 2011. Multi-criteria Group Decision Supplier Selection Problem Using Fuzzy TOPSIS Based Approach. Zouggari, A., Benyoucef, L.,(2011) Multi-Criteria Group Decision Supplier Selection Problem using Fuzzy Topsis based Approach,EUSFLAT-LFA, pp.628-635. 59 APPENDICES 61 APPENDIX A1 : Questionnaire Questionnaire Read the following questions and put check marks on the pairwise comparison matrices. If an attribute on the left is more important than the one matching on the right, put your check mark to the left of the importance ‘‘Equal’’ under the importance level you prefer. If an attribute on the left is less important than the one matching on the right, put your check mark to the right of the importance ‘‘Equal’’ under the importance level you prefer. QUESTIONS FOR FIRST DECISION MAKER With respect to the overall goal ‘‘Selection of Appropriate Candidates for Surgical Sciences’’, Q1. How important is Knowledge (C1) when it is compared with Skill (C2)? Q2. How important is Knowledge (C1) when it is compared with Ability (C3)? Q3. How important is Skill (C2) when it is compared with Ability (C3)? With respect to the main attribute ‘‘Knowledge (C1)’’, Q1. How important is Occupational Knowledge (C11) when it is compared with Foreign Language Knowledge (C12)? Q2. How important is Occupational Knowledge (C11) when it is compared with Graduated School (C13)? Q3. How important is Occupational Knowledge (C11) when it is compared with Academic Publishing (C14)? Q4. How important is Foreign Language Knowledge (C12) when it is compared with Graduated School (C13)? Q5. How important is Foreign Language Knowledge (C12) when it is compared with Academic Publishing (C14)? Q6. How important is Graduated School (C13) when it is compared with Academic Publishing (C14)? 62 With respect to the main attribute ‘‘Skill (C2)’’, Q1. How important is Basic Skills (C21) when it is compared with Complex Problem Solving Skills (C22)? Q2. How important is Basic Skills (C21) when it is compared with System Skills (C23)? Q3. How important is Basic Skills (C21) when it is compared with Experience (C24)? Q4. How important is Basic Skills (C21) when it is compared with Number of Case (C25)? Q5. How important is Basic Skills (C21) when it is compared with Success rate of Cases (C26)? Q6. How important is Basic Skills (C21) when it is compared with Stabilisation (C27)? Q7. How important is Basic Skills (C21) when it is compared with Reference (C28)? Q8. How important is Complex Problem Solving Skills (C22) when it is compared with System Skills (C23)? Q9. How important is Complex Problem Solving Skills (C22) when it is compared with Experience (C24)? Q10. How important is Complex Problem Solving Skills (C22) when it is compared with Number of Case (C25)? Q11. How important is Complex Problem Solving Skills (C22) when it is compared with Success rate of Cases (C26)? Q12. How important is Complex Problem Solving Skills (C22) when it is compared with Stabilisation (C27)? Q13. How important is Complex Problem Solving Skills (C22) when it is compared with Reference (C28)? Q14. How important is System Skills (C23) when it is compared with Experience (C24)? Q15. How important is System Skills (C23) when it is compared with Number of Case (C25)? 63 Q16. How important is System Skills (C23) when it is compared with Success rate of Cases (C26)? Q17. How important is System Skills (C23) when it is compared with Stabilisation (C27)? Q18. How important is System Skills (C23) when it is compared with Reference (C28)? Q19. How important is Experience (C24) when it is compared with Number of Case (C25)? Q20. How important is Experience (C24) when it is compared with Success rate of Cases (C26)? Q21. How important is Experience (C24) when it is compared with Stabilisation (C27)? Q22. How important is Experience (C24) when it is compared with Reference (C28)? Q23. How important is Number of Case (C25) when it is compared with Success rate of Cases (C26)? Q24. How important is Number of Case (C25) when it is compared with Stabilisation (C27)? Q25. How important is Number of Case (C25) when it is compared with Reference (C28)? Q26. How important is Success rate of Cases (C26) when it is compared with Stabilisation (C27)? Q27. How important is Success rate of Cases (C26) when it is compared with Reference (C28)? Q28. How important is Success to Stabilisation (C27) when it is compared with Reference (C28)? With respect to the main attribute ‘‘Ability (C3)’’, Q1. How important is Psychomotor Abilities (C31) when it is compared with Cognitive Abilities (C32)? 64 Q2. How important is Psychomotor Abilities (C31) when it is compared with Managerial Competence (C33)? Q3. How important is Cognitive Abilities (C32) when it is compared with Managerial Competence (C33)? With respect to the sub-attribute ‘‘(Cxy)’’, respectively, Q1. How important is A1 when it is compared with A2 and A3? Q2. How important is A2 when it is compared with A1 and A3? Q3. How important is A3 when it is compared with A1 and A2? QUESTIONS FOR SECOND DECISION MAKER With respect to the overall goal ‘‘Selection of Appropriate Candidates for Surgical Sciences’’, Q1. How important is Knowledge (C1) when it is compared with Skill (C2)? Q2. How important is Knowledge (C1) when it is compared with Ability(C3)? Q3. How important is Skill (C2) when it is compared with Ability (C3)? With respect to the main attribute ‘‘Knowledge (C1)’’, Q1. How important is Occupational Knowledge (C11) when it is compared with Foreign Language Knowledge (C12)? Q2. How important is Occupational Knowledge (C11) when it is compared with Graduated School (C13)? Q3. How important is Occupational Knowledge (C11) when it is compared with Academic Publishing (C14)? Q4. How important is Foreign Language Knowledge (C12) when it is compared with Graduated School (C13)? Q5. How important is Foreign Language Knowledge (C12) when it is compared with Academic Publishing (C14)? 65 Q6. How important is Graduated School (C13) when it is compared with Academic Publishing (C14)? With respect to the main attribute ‘‘Skill (C2)’’, Q1. How important is Basic Skills (C21) when it is compared with Complex Problem Solving Skills (C22)? Q2. How important is Basic Skills (C21) when it is compared with System Skills (C23)? Q3. How important is Basic Skills (C21) when it is compared with Experience (C24)? Q4. How important is Basic Skills (C21) when it is compared with Number of Case (C25)? Q5. How important is Basic Skills (C21) when it is compared with Success rate of Cases (C26)? Q6. How important is Basic Skills (C21) when it is compared with Stabilisation (C27)? Q7. How important is Basic Skills (C21) when it is compared with Reference (C28)? Q8. How important is Complex Problem Solving Skills (C22) when it is compared with System Skills (C23)? Q9. How important is Complex Problem Solving Skills (C22) when it is compared with Experience (C24)? Q10. How important is Complex Problem Solving Skills (C22) when it is compared with Number of Case (C25)? Q11. How important is Complex Problem Solving Skills (C22) when it is compared with Success rate of Cases (C26)? Q12. How important is Complex Problem Solving Skills (C22) when it is compared with Stabilisation (C27)? Q13. How important is Complex Problem Solving Skills (C22) when it is compared with Reference (C28)? Q14. How important is System Skills (C23) when it is compared with Experience (C24)? 66 Q15. How important is System Skills (C23) when it is compared with Number of Case (C25)? Q16. How important is System Skills (C23) when it is compared with Success rate of Cases (C26)? Q17. How important is System Skills (C23) when it is compared with Stabilisation (C27)? Q18. How important is System Skills (C23) when it is compared with Reference (C28)? Q19. How important is Experience (C24) when it is compared with Number of Case (C25)? Q20. How important is Experience (C24) when it is compared with Success rate of Cases (C26)? Q21. How important is Experience (C24) when it is compared with Stabilisation (C27)? Q22. How important is Experience (C24) when it is compared with Reference (C28)? Q23. How important is Number of Case (C25) when it is compared with Success rate of Cases (C26)? Q24. How important is Number of Case (C25) when it is compared with Stabilisation (C27)? Q25. How important is Number of Case (C25) when it is compared with Reference (C28)? Q26. How important is Success rate of Cases (C26) when it is compared with Stabilisation (C27)? Q27. How important is Success rate of Cases (C26) when it is compared with Reference (C28)? Q28. How important is Success to Stabilisation (C27) when it is compared with Reference (C28)? With respect to the main attribute ‘‘Ability (C3)’’, 67 Q1. How important is Psychomotor Abilities (C31) when it is compared with Cognitive Abilities (C32)? Q2. How important is Psychomotor Abilities (C31) when it is compared with Managerial Competence (C33)? Q3. How important is Cognitive Abilities (C32) when it is compared with Managerial Competence (C33)? With respect to the sub-attribute ‘‘(Cxy)’’, respectively, Q4. How important is A1 when it is compared with A2 and A3? Q5. How important is A2 when it is compared with A1 and A3? Q6. How important is A3 when it is compared with A1 and A2? 68 APPENDIX A2 : Pairwise Comparisons For Decision Criteria Pairwise Comparison for selecting criteria in surgeon selection problem by first decision maker Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Knowledge X Skills Knowledge X Abilities Skills X Abilities Pairwise Comparison for selecting criteria in surgeon selection problem by second decision maker Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Knowledge X Skills Knowledge X Abilities Skills X Abilities 69 Pairwise Comparison for criterias in surgeon selection problem by first decision maker Knowledge Importance (or preference) of one sub-attribute over another Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Occupational Knowledge X Foreign Language Knowledge Occupational Knowledge X Graduated School Occupational Knowledge X Academic Publishing Foreign Language X Graduated School Foreign Language X Academic Publishing Graduated School X Academic Publishing 70 Pairwise Comparison for criterias in surgeon selection problem by second decision maker Knowledge Importance (or preference) of one sub-attribute over another Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Occupational Knowledge X Foreign Language Knowledge Occupational Knowledge X Graduated School Occupational Knowledge X Academic Publishing Foreign Language X Graduated School Foreign Language X Academic Publishing Graduated School X Academic Publishing 71 Pairwise Comparison for criterias in surgeon selection problem by first decision maker Skills Importance (or preference) of one sub-attribute over another Criteria A bs ol ut el y Im po rt an t V er y St ro ng ly Im po rt an t E ss en tia lly Im po rt an t W ea kl y Im po rt an t E qu al ly Im po rt an t Ju st E qu al E qu al ly Im po rt an t W ea kl y Im po rt an t E ss en tia lly Im po rt an t V er y St ro ng ly I t t A bs ol ut el y Im po rt an t Criteria Basic Skills X Complex Problem Solving Skills Basic Skills X System Skills Basic Skills X Experience Basic Skills X Number of Case Basic Skills X Success rate of Cases Basic Skills X Stabilisation Basic Skills X Reference Complex Problem Solving Skills X System Skills Complex Problem Solving Skills X Experience Complex Problem Solving Skills X Number of Case Complex Problem Solving Skills X Success rate of Cases Complex Problem Solving Skills X Stabilisation Complex Problem Solving Skills X Reference System Skills X Experience System Skills X Number of Case System Skills X Success rate of Cases System Skills X Stabilisation System Skills X Reference 72 Experience X Number of Case Experience X Success rate of Cases Experience X Stabilisation Experience X Reference Number of Case X Success rate of Cases Number of Case X Stabilisation Number of Case X Reference Success rate of Cases X Stabilisation Success rate of Cases X Reference Stabilisation X Reference 73 Pairwise Comparison for criterias in surgeon selection problem by second decision maker Skills Importance (or preference) of one sub-attribute over another Criteria A bs ol ut el y Im po rt an t V er y St ro ng ly Im po rt an t E ss en tia lly Im po rt an t W ea kl y Im po rt an t E qu al ly Im po rt an t Ju st E qu al E qu al ly Im po rt an t W ea kl y Im po rt an t E ss en tia lly Im po rt an t V er y St ro ng ly Im po rt an t A bs ol ut el y Im po rt an t Criteria Basic Skills X Complex Problem Solving Skills Basic Skills X System Skills Basic Skills X Experience Basic Skills X Number of Case Basic Skills X Success rate of Cases Basic Skills X Stabilisation Basic Skills X Reference Complex Problem Solving Skills X System Skills Complex Problem Solving Skills X Experience Complex Problem Solving Skills X Number of Case Complex Problem Solving Skills X Success rate of Cases Complex Problem Solving Skills X Stabilisation Complex Problem Solving Skills X Reference System Skills X Experience System Skills X Number of Case 74 System Skills X Success rate of Cases System Skills X Stabilisation System Skills X Reference Experience X Number of Case Experience X Success rate of Cases Experience X Stabilisation Experience X Reference Number of Case X Success rate of Cases Number of Case X Stabilisation Number of Case X Reference Success rate of Cases X Stabilisation Success rate of Cases X Reference Stabilisation X Reference 75 Pairwise Comparison for criterias in surgeon selection problem by first decision maker Abilities Importance (or preference) of one sub-attribute over another Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Psychomotor Abilities X Cognitive Abilities Psychomotor Abilities X Managerial Competence Cognitive Abilities X Managerial Competence Pairwise Comparison for criterias in surgeon selection problem by second decision maker Abilities Importance (or preference) of one sub-attribute over another Criteria A b s o l u t e l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t W e a k l y I m p o r t a n t E q u a l l y I m p o r t a n t J u s t E q u a l E q u a l l y I m p o r t a n t W e a k l y I m p o r t a n t E s s e n t i a l l y I m p o r t a n t V e r y S t r o n g l y I m p o r t a n t A b s o l u t e l y I m p o r t a n t Criteria Psychomotor Abilities X Cognitive Abilities Psychomotor Abilities X Managerial Competence Cognitive Abilities X Managerial Competence 76 APPENDIX A3: Pairwise Comparisons for Decision Criteria With Fuzzy Number Pairwise Comparison of Main Goal for criteria in surgeon selection problem by first decision maker with Fuzzy Numbers Goal Knowledge Skills Abilities Knowledge (1,1,1) (5,7,9)-1 (3,5,7)-1 Skills (5,7,9) (1,1,1) (1,1,3) Abilities (3,5,7) (1,1,3)-1 (1,1,1) Pairwise Comparison of Main Goal for criteria in surgeon selection problem by second decision maker with Fuzzy Numbers Goal Knowledge Skills Abilities Knowledge (1,1,1) (3,5,7)-1 (1,3,5)-1 Skills (3,5,7) (1,1,1) (1,1,3) Abilities (1,3,5) (1,1,3)-1 (1,1,1) Fuzzy Aggregated Decision Matrix Knowledge Skills Abilities Knowledge 1.00 1.00 1.00 0.12 0.17 0.26 0.17 0.26 0.57 Skills 3.87 5.92 7.94 1.00 1.00 1.00 1.00 1.00 3.00 Abilities 1.73 3.87 5.92 0.33 1.00 1.00 1.00 1.00 1.00 77 Pairwise Comparison criteria of Knowledge for sub-criteria in surgeon selection problem by first decision maker with Fuzzy Numbers Knowledge Occupational Knowledge Foreign Language Knowledge Graduated School Academic Publishing Occupational Knowledge (1,1,1) (7,9,9) (3,5,7)-1 (3,5,7) Foreign Language Knowledge (7,9,9)-1 (1,1,1) (5,7,9)-1 (3,5,7)-1 Graduated School (3,5,7) (5,7,9) (1,1,1) (5,7,9) Academic Publishing (3,5,7)-1 (3,5,7) (5,7,9)-1 (1,1,1) Pairwise Comparison criteria of Knowledge for sub-criteria in surgeon selection problem by second decision maker with Fuzzy Numbers Knowledge Occupational Knowledge Foreign Language Knowledge Graduated School Academic Publishing Occupational Knowledge (1,1,1) (3,5,7) (3,5,7) (3,5,7) Foreign Language Knowledge (3,5,7)-1 (1,1,1) (3,5,7)-1 (1,3,5)-1 Graduated School (3,5,7)-1 (3,5,7) (1,1,1) (1,3,5) Academic Publishing (3,5,7)-1 (1,3,5) (1,3,5)-1 (1,1,1) 78 Fuzzy Aggregated Decision Matrix Pairwise Comparison criteria of Skills for sub-criteria in surgeon selection problem by first decision maker with Fuzzy Numbers Skills Basic Skills Comple x Problem Solving Skills Syste m Skills Experienc e Number of Case Success rate of Cases Stabilisatio n Reference Basic Skills (1,1,1) (1,3,5) (3,5,7) (3,5,7)-1 (1,1,3) (5,7,9)-1 (3,5,7)-1 (1,3,5)-1 Complex Problem Solving Skills (1,3,5)-1 (1,1,1) (5,7,9) (3,5,7)-1 (3,5,7) (5,7,9)-1 (3,5,7)-1 (1,1,3) System Skills (3,5,7)-1 (5,7,9)-1 (1,1,1) (5,7,9)-1 (1,3,5)-1 (7,9,9)-1 (3,5,7)-1 (5,7,9)-1 Experien ce (3,5,7) (3,5,7) (5,7,9) (1,1,1) (1,1,3) (5,7,9)-1 (3,5,7)-1 (3,5,7) Number of Case (1,1,3)-1 (3,5,7)-1 (1,3,5) (1,1,3)-1 (1,1,1) (3,5,7)-1 (1,3,5)-1 (3,5,7)-1 Success rate of Cases (5,7,9) (5,7,9) (7,9,9,) (5,7,9) (3,5,7) (1,1,1) (5,7,9)-1 (1,3,5) Stabilisat ion (3,5,7) (3,5,7) (3,5,7) (3,5,7) (1,3,5) (5,7,9) (1,1,1) (3,5,7) Referenc e (1,3,5) (1,1,3)-1 (5,7,9) (3,5,7)-1 (3,5,7) (1,3,5)-1 (3,5,7)-1 (1,1,1) Occupational Knowledge Foreign Language Knowledge Graduated School Academic Publishing Occupational Knowledge 1.00 1.00 1.00 4.58 6.71 7.94 0.65 1.00 1.52 3.00 5.00 7.00 Foreign Language Knowledge 0.12 0.15 0.21 1.00 1.00 1.00 0.12 0.17 0.26 0.17 0.26 0.57 Graduated School 0.65 1.00 1.52 3.87 5.92 7.94 1.00 1.00 1.00 2.24 4.58 6.71 Academic Publishing 0.14 0.20 0.33 1.73 3.87 5.92 0.15 0.21 0.45 1.00 1.00 1.00 79 Pairwise Comparison criteria of Skills for sub-criteria in surgeon selection problem by second decision maker with Fuzzy Numbers Skills Basic Skills Complex Problem Solving Skills System Skills Experie nce Number of Case Success rate of Cases Stabilisation Reference Basic Skills (1,1,1) (3,5,7)-1 (1,3,5)-1 (5,7,9)-1 (5,7,9)-1 (5,7,9)-1 (5,7,9)-1 (1,3,5)-1 Complex Problem Solving Skills (3,5,7) (1,1,1) (3,5,7) (1,3,5) (1,3,5) (1,1,3) (1,3,5) (1,3,5) System Skills (1,3,5) (3,5,7)-1 (1,1,1) (1,3,5)-1 (3,5,7)-1 (3,5,7)-1 (3,5,7)-1 (1,3,5)-1 Experience (5,7,9) (1,3,5)-1 (1,3,5) (1,1,1) (1,1,3) (1,3,5)-1 (1,3,5) (1,3,5) Number of Case (5,7,9) (1,3,5)-1 (3,5,7) (1,1,3)-1 (1,1,1) (5,7,9)-1 (3,5,7) (3,5,7) Success rate of Cases (5,7,9) (1,1,3)-1 (3,5,7) (1,3,5) (5,7,9) (1,1,1) (3,5,7) (3,5,7) Stabilisation (5,7,9) (1,3,5)-1 (3,5,7) (1,3,5)-1 (3,5,7)-1 (3,5,7)-1 (1,1,1) (1,3,5) Reference (1,3,5) (1,3,5)-1 (1,3,5) (1,3,5)-1 (3,5,7)-1 (3,5,7)-1 (1,3,5)-1 (1,1,1) 80 Fuzzy Aggregated Decision Matrix Basic Skills Complex Problem Solvin g Skill s System Skills Experie n ce Number of Case Success rate of Cases Stabili s a t i o n Referen c e Basic Skills 1.00 1.00 1.00 0.37 0.77 1.28 0.77 1.28 2.65 0.12 0.17 0.26 0.33 0.37 0.77 0.11 0.14 0.20 0.12 0.17 0.26 0.20 0.33 1.00 Complex Problem Solving Skills 0.77 1.28 2.65 1.00 1.00 1.00 3.87 5.92 7.94 0.37 0.77 1.28 1.73 3.87 5.92 0.33 0.37 0.77 0.37 0.77 1.28 1.00 1.73 3.87 S ys t e m Skills 0.37 0.77 1.28 0.12 0.17 0.26 1.00 1.00 1.00 0.15 0.21 0.45 0.17 0.26 0.57 0.12 0.17 0.26 0.14 0.20 0.33 0.15 0.21 0.45 Experience 3.87 5.92 7.94 0.77 1.28 2.65 2.24 4.58 6.71 1.00 1.00 1.00 1.00 1.00 3.00 0.15 0.21 0.45 0.37 0.77 1.28 1.73 3.87 5.92 N u mbe r of Case 1.28 2.65 3.00 0.17 0.26 0.57 1.73 3.87 5.92 0.33 1.00 1.00 1.00 1.00 1.00 0.12 0.17 0.26 0.77 1.28 2.65 0.65 1.00 1.52 S u c c e ss rate of Cases 5.00 7.00 9.00 1.28 2.65 3.00 4.58 6.71 7.94 2.24 4.58 6.71 3.87 5.92 7.94 1.00 1.00 1.00 0.57 0.84 1.18 1.73 3.87 5.92 Stabilisation 3.87 5.92 7.94 0.77 1.28 2.65 3.00 5.00 7.00 0.77 1.28 2.65 0.37 0.77 1.28 0.84 1.18 1.72 1.00 1.00 1.00 1.73 3.87 5.92 R ef e r en c e 1.00 3.00 5.00 0.26 0.57 1.00 2.24 4.58 6.71 0.17 0.26 0.57 0.65 1.00 1.52 0.17 0.26 0.57 0.17 0.26 0.57 1.00 1.00 1.00 81 Pairwise Comparison criteria of Abilities for sub-criteria in surgeon selection problem by first decision maker with Fuzzy Numbers Abilities Psychomotor Abilities Cognitive Abilities Managerial Competence Psychomotor Abilities (1,1,1) (1,3,5)-1 (3,5,7)-1 Cognitive Abilities (1,3,5) (1,1,1) (1,3,5)-1 Managerial Competence (3,5,7) (1,3,5) (1,1,1) Pairwise Comparison criteria of Abilities for sub-criteria in surgeon selection problem by second decision maker with Fuzzy Numbers Abilities Psychomotor Abilities Cognitive Abilities Managerial Competence Psychomotor Abilities (1,1,1) (1,3,5) (3,5,7) Cognitive Abilities (1,3,5)-1 (1,1,1) (1,1,3) Managerial Competence (3,5,7)-1 (1,1,3)-1 (1,1,1) Fuzzy Aggregated Decision Matrix Psychomotor Abilities Cognitive Abilities Managerial Competence Psychomotor Abilities 1.00 1.00 1.00 0.45 0.99 2.24 0.65 1.00 1.52 Cognitive Abilities 0.45 0.99 2.24 1.00 1.00 1.00 0.45 0.57 1.73 Managerial Competence 0.65 1.00 1.52 0.57 1.73 2.24 1.00 1.00 1.00 82 Fuzzy Weight Matrix Occupational Knowledge 0,23 0,43 0,77 Foreign Language Knowledge 0,03 0,05 0,11 Graduated School 0,21 0,41 0,76 Academic Publishing 0,06 0,11 0,25 Basic Skills 0,01 0,03 0,10 Complex Problem Solving Skills 0,05 0,13 0,39 System Skills 0,01 0,02 0,07 Experience 0,05 0,14 0,44 Number of Case 0,03 0,08 0,22 Success rate of Cases 0,13 0,34 0,78 Stabilisation 0,07 0,19 0,52 Reference 0,02 0,07 0,21 Psychomotor Abilities 0,14 0,33 0,76 Cognitive Abilities 0,13 0,27 0,80 Managerial Competence 0,16 0,40 0,76 83 APPENDIX A4: Curriculum Vitae Of Candidates Cv of 1st Candidate General Surgery - Organ Transplant Specialist The Task Received Medical Units : General Surgery, Organ Transplantation Place and Date of Birth : Çanakkale, Turkey / 1974 Foreign Languages : English Experience 2005 – Halen Specialist General Surgery and Organ Transplantation, Organ Transplant Center İstanbul/Turkey 2004 – 2005 General Surgeon – reserve officer Diyarbakır/Turkey 2004 – 2004 General Surgeon İstanbul/Turkey Education 1998 - 2003 General Surgery Residency Training İstanbul/Turkey 1992 - 1998 Education of Medical Doctor İstanbul/Turkey Professional Training Attended, Courses and Conferences • Vascular Repair Techniques, Practical Training Course, 2004 • 5th and 7th Colon and Rectal Diseases, Postgraduate Education Course, 2000 / 2004 • 2nd Trauma and Emergency Surgery Postgraduate Education Course, 2001 • 11. Postgraduate of Breast Diseases training course, 2006 • participation national and international congresses and symposium Professional Awards and Levels Proof of proficiency of Turkish Surgery ( BOARD ) (2005 / 1080) 84 Professional Memberships • Society of Turkish Surgery • Organ Transplant Association of Turkey • Society of Emergency Surgery and Traumatology Scientific Publications • Publication of 20 national and international journals, presented with 18 oral presentations at various conferencesand 12 poster presentation. Two sections of written in the books of Laparoscopic Surgery. 85 Cv of 2nd Candidate Head of the Department of Plastic Surgery The Task Received Medical Units : Aesthetic Plastic and Reconstructive Surgery Place and Date of Birth : İstanbul, Turkey / 1959 Foreign Languages : English Experience 2011 – Still Head of the Department of Plastic Surgery İstanbul/Turkey 2002 – 2011 Aesthetic Plastic and Reconstructive Surgeon – reserve officer Diyarbakır/Turkey 1992 – 2002 Instructor-Aesthetic Plastic and Reconstructive Surgeon İstanbul/Turkey 1983 - 1985 Compulsory duties Ordu/Turkey Education 1997 - Still Associate Professor İstanbul/Turkey 1985 - 1990 Plastic and Reconstructive Surgery Residency Training İstanbul/Turkey 1977 - 1983 Education of Medical Doctor Ankara/Turkey Professional Training Attended, Courses and Conferences • 1990 – 1991 University of Alabama at Birmingham, Fellow Clinical and Research • Has given over 100 international conferences as an invited speaker at the congress. 86 Professional Memberships v. Head of the Turkish Society of Aesthetic Plastic Surgery. vi. ISAPS (International Society of Aesthetic Plastic Surgery) Education Council Chair - Education Committee Chairman and Board Member vii. Plastic Reconstructive Surgery Journal (American Plastic Association of surgeons – ASPS – Official Journal) Editorial Board Member 87 Cv of 3rd Candidate Brain and Neurological Surgery Specialist The Task Received Medical Units : Brain Surgery Place and Date of Birth : Erzurum, Turkey / 1966 Foreign Languages : English Experience 2010 – Still Brain and Neurological Surgery Specialist Antalya/Turkey 2008 – 2010 Brain and Neurological Surgery Specialist Istanbul/Turkey 2005 – 2008 Brain and Neurological Surgery Specialist İstanbul/Turkey 2004 - 2005 Brain and Neurological Surgery Specialist Istanbul/Turkey 2001-2004 Lecturer, Department of Neurological Surgery Ankara/Turkey 1999-2001 Brain and Neurological Surgery Specialist Istanbul/Turkey Education 1994 - 1999 Neurosurgery Residency Training İstanbul/Turkey 1983 - 1989 Education of Medical Doctor İzmir/Turkey Professional Training Attended, Courses and Conferences • Turkey Board of Neurosurgery • Pediatric Neurosurgery • Microsurgery Laboratory Study Professional Memberships viii. Turkish Society of Neurosurgery ix. The Turkish Medical Association 88 Scientific Publications iii. Writing the Book Section, Spinal Infections iv. 6 pieces of published papers in international refereed journals, international conference speech, 8 national publications, 35 papers in national conferences. 89 APPENDIX A5: Assesment of Decision Makers for Candidates Evaluation of alternatives with respect to Occupational Knowledge Occupational Knowledge D1 D2 A1 MG F A2 VG VG A3 G MG Evaluation of alternatives with respect to Foreign Language Knowlegde Foreign Language Knowledge D1 D2 A1 F G A2 G VG A3 F F Evaluation of alternatives with respect to Graduated School Graduated School D1 D2 A1 F MG A2 VG G A3 G G 90 Evaluation of alternatives with respect to Academic Publishing Academic Publishing D1 D2 A1 G G A2 VG VG A3 F MP Evaluation of alternatives with respect to Basic Skills Basic Skills D1 D2 A1 F F A2 G G A3 VG G Evaluation of alternatives with respect to Complex Problem Solving Skills Complex Problem Solving Skills D1 D2 A1 MG VG A2 G MG A3 G G 91 Evaluation of alternatives with respect to System Skills System Skills D1 D2 A1 G G A2 MG G A3 MG F Evaluation of alternatives with respect to Experience Experience D1 D2 A1 F MG A2 VG VG A3 G G Evaluation of alternatives with respect to Number of Case Number of Case D1 D2 A1 F F A2 G G A3 MG MG 92 Evaluation of alternatives with respect to Success rate of Cases Success rate of Cases D1 D2 A1 G G A2 G G A3 MG MG Evaluation of alternatives with respect to Stabilisation Stabilisation D1 D2 A1 F VG A2 VG G A3 F MG Evaluation of alternatives with respect to Reference Reference D1 D2 A1 G G A2 G G A3 G G 93 Evaluation of alternatives with respect to Psychomotor Abilities Psychomotor Abilities D1 D2 A1 G G A2 G G A3 VG VG Evaluation of alternatives with respect to Cognitive Abilities Cognitive Abilities D1 D2 A1 G MG A2 G G A3 G G Evaluation of alternatives with respect to Managerial Competence Managerial Competence D1 D2 A1 G MG A2 VG VG A3 G G 94 APPENDIX A6: Assesment of Decision Makers for Candidates with Fuzzy Numbers Ratings of alternatives with respect to Occupational Knowledge with Fuzzy Numbers Occupational Knowledge D1 D2 A1 (5,7,9) (3,5,7) A2 (9,10,10) (9,10,10) A3 (7,9,10) (5,7,9) Ratings of alternatives with respect to Foreign Language Knowlegde with Fuzzy Numbers Foreign Language Knowledge D1 D2 A1 (3,5,7) (7,9,10) A2 (7,9,10) (9,10,10) A3 (3,5,7) (3,5,7) Ratings of alternatives with respect to Graduated School with Fuzzy Numbers Graduated School D1 D2 A1 (3,5,7) (5,7,9) A2 (9,10,10) (7,9,10) A3 (7,9,10) (7,9,10) 95 Ratings of alternatives with respect to Academic Publishing with Fuzzy Numbers Academic Publishing D1 D2 A1 (7,9,10) (7,9,10) A2 (9,10,10) (9,10,10) A3 (3,5,7) (1,3,5) Ratings of alternatives with respect to Basic Skills with Fuzzy Numbers Basic Skills D1 D2 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) A3 (9,10,10) (7,9,10) Ratings of alternatives with respect to Complex Problem Solving Skills with Fuzzy Numbers Complex Problem Solving Skills D1 D2 A1 (5,7,9) (9,10,10) A2 (7,9,10) (5,7,9) A3 (7,9,10) (7,9,10) 96 Ratings of alternatives with respect to System Skills with Fuzzy Numbers System Skills D1 D2 A1 (7,9,10) (7,9,10) A2 (5,7,9) (7,9,10) A3 (5,7,9) (3,5,7) Ratings of alternatives with respect to Experience with Fuzzy Numbers Experience D1 D2 A1 (3,5,7) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) Ratings of alternatives with respect to Number of Case with Fuzzy Numbers Number of Case D1 D2 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) A3 (5,7,9) (5,7,9) 97 Ratings of alternatives with respect to Success rate of Cases with Fuzzy Numbers Success rate of Cases D1 D2 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (5,7,9) (5,7,9) Ratings of alternatives with respect to Stabilisation with Fuzzy Numbers Stabilisation D1 D2 A1 (3,5,7) (9,10,10) A2 (9,10,10) (7,9,10) A3 (3,5,7) (5,7,9) Ratings of alternatives with respect to Reference with Fuzzy Numbers Reference D1 D2 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) 98 Ratings of alternatives with respect to Psychomotor Abilities with Fuzzy Numbers Psychomotor Abilities D1 D2 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (9,10,10) (9,10,10) Ratings of alternatives with respect to Cognitive Abilities with Fuzzy Numbers Cognitive Abilities D1 D2 A1 (7,9,10) (5,7,9) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) Ratings of alternatives with respect to Managerial Competence with Fuzzy Numbers Managerial Competence D1 D2 A1 (7,9,10) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) 99 APPENDIX A7: Ratings of Candidates by Decision Makers The ratings of the three candidates by decision makers under all criteria Criteria Candidates Decision Makers D1 D2 C11 A1 MG F A2 VG VG A3 G MG C12 A1 F G A2 G VG A3 F F C13 A1 F MG A2 VG G A3 G G C14 A1 G G A2 VG VG A3 F MP C21 A1 F F A2 G G A3 VG G C22 A1 MG VG A2 G MG A3 G G C23 A1 G G A2 MG G A3 MG F C24 A1 F MG A2 VG VG A3 G G C25 A1 F F A2 G G A3 MG MG C26 A1 G G A2 G G A3 MG MG C27 A1 F VG A2 VG G A3 F MG C28 A1 G G A2 G G 100 A3 G G C31 A1 G G A2 G G A3 VG VG C32 A1 G MG A2 G G A3 G G C33 A1 G MG A2 VG VG A3 G G The ratings of the three candidates by decision makers under all criteria Criteria Candidates Decision Makers D1 D2 C11 A1 (5,7,9) (3,5,7) A2 (9,10,10) (9,10,10) A3 (7,9,10) (5,7,9) C12 A1 (3,5,7) (7,9,10) A2 (7,9,10) (9,10,10) A3 (3,5,7) (3,5,7) C13 A1 (3,5,7) (5,7,9) A2 (9,10,10) (7,9,10) A3 (7,9,10) (7,9,10) C14 A1 (7,9,10) (7,9,10) A2 (9,10,10) (9,10,10) A3 (3,5,7) (1,3,5) C21 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) A3 (9,10,10) (7,9,10) C22 A1 (5,7,9) (9,10,10) A2 (7,9,10) (5,7,9) A3 (7,9,10) (7,9,10) C23 A1 (7,9,10) (7,9,10) A2 (5,7,9) (7,9,10) A3 (5,7,9) (3,5,7) C24 A1 (3,5,7) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) C25 A1 (3,5,7) (3,5,7) A2 (7,9,10) (7,9,10) 101 A3 (5,7,9) (5,7,9) C26 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (5,7,9) (5,7,9) C27 A1 (3,5,7) (9,10,10) A2 (9,10,10) (7,9,10) A3 (3,5,7) (5,7,9) C28 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) C31 A1 (7,9,10) (7,9,10) A2 (7,9,10) (7,9,10) A3 (9,10,10) (9,10,10) C32 A1 (7,9,10) (5,7,9) A2 (7,9,10) (7,9,10) A3 (7,9,10) (7,9,10) C33 A1 (7,9,10) (5,7,9) A2 (9,10,10) (9,10,10) A3 (7,9,10) (7,9,10) 102 APPENDIX A8: Fuzzy Decision Matrix of Alternatives with TOPSIS The fuzzy decision matrix and fuzzy weights of three alternatives C11 C12 C13 C14 C21 A 1 (4.00 6.00 8.00) (5.00 7.00 8.50) (4.00 6.00 8.00) (7.00 9.00 10.00) (3.00 5.00 7.00) A 2 (9.00 10.00 10.00) (8.00 9.50 10.00) (8.00 9.50 10.00) (9.00 10.00 10.00) (7.00 9.00 10.00) A 3 (6.00 8.00 9.50) (3.00 5.00 7.00) (7.00 9.00 10.00) (2.00 4.00 6.00) (8.00 9.50 10.00) C22 C23 C24 C25 C26 A 1 (7.00 8.50 9.50) (7.00 9.00 10.00) (4.00 6.00 8.00) (3.00 5.00 7.00) (7.00 9.00 10.00) A 2 (6.00 8.00 9.50) (6.00 8.00 9.50) (9.00 10.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) A 3 (7.00 9.00 10.00) (4.00 6.00 8.00) (7.00 9.00 10.00) (5.00 7.00 9.00) (5.00 7.00 9.00) C27 C28 C31 C32 C33 A 1 (6.00 7.50 8.50) (7.00 9.00 10.00) (7.00 9.00 10.00) (6.00 8.00 9.50) (6.00 8.00 9.50) A 2 (8.00 9.50 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) (9.00 10.00 10.00) A 3 (4.00 6.00 8.00) (7.00 9.00 10.00) (9.00 10.00 10.00) (7.00 9.00 10.00) (7.00 9.00 10.00) 103 The Fuzzy Normalized Decision Matrix C11 C12 C13 C14 C21 A 1 (0.40 0.60 0.80) (0.50 0.70 0.85) (0.40 0.60 0.80) (0.70 0.90 1.00) (0.30 0.50 0.70) A 2 (0.90 1.00 1.00) (0.80 0.95 1.00) (0.80 0.95 1.00) (0.90 1.00 1.00) (0.70 0.90 1.00) A 3 (0.60 0.80 0.95) (0.30 0.50 0.70) (0.70 0.90 1.00) (0.20 0.40 0.60) (0.80 0.95 1.00) C27 C28 C31 C32 C33 A 1 (0.60 0.75 0.85) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.60 0.80 0.95) (0.60 0.80 0.95) A 2 (0.80 0.95 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) (0.90 1.00 1.00) A 3 (0.40 0.60 0.80) (0.70 0.90 1.00) (0.90 1.00 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) C22 C23 C24 C25 C26 A 1 (0.70 0.85 0.95) (0.70 0.90 1.00) (0.40 0.60 0,80) (0.30 0.50 0.70) (0.70 0.90 1.00) A 2 (0.60 0.80 0.95) (0.60 0.80 0.95) (0.90 1.00 1.00) (0.70 0.90 1.00) (0.70 0.90 1.00) A 3 (0.70 0.90 1.00) (0.40 0.60 0.80) (0.70 0.90 1.00) (0.50 0.70 0.90) (0.50 0.70 0.90) 104 The Fuzzy Weighted Normalized Matrix The Distance Measurement C11 C12 C13 C14 C21 A 1 (0,00 0,02 0,12) (0,00 0,00 0,02) (0,00 0,02 0,12) (0,00 0,01 0,05) (0,00 0,01 0,07) A 2 (0,01 0,04 0,15) (0,00 0,00 0,02) (0,01 0,03 0,15) (0,00 0,01 0,05) (0,00 0,01 0,10) A 3 (0,01 0,03 0,15) (0,00 0,00 0,02) (0,01 0,03 0,15) (0,00 0,00 0,03) (0,00 0,02 0,10) C22 C23 C24 C25 C26 A 1 (0,01 0,06 0,40) (0,00 0,01 0,07) (0,01 0,05 0,38) (0,00 0,02 0,16) (0,03 0,17 0,84) A 2 (0,01 0,06 0,40) (0,00 0,01 0,07) (0,01 0,08 0,47) (0,01 0,04 0,23) (0,03 0,17 0,84) A 3 (0,01 0,06 0,42) (0,00 0,01 0,06) (0,01 0,07 0,47) (0,00 0,03 0,21) (0,02 0,13 0,75) C27 C28 C31 C32 C33 A 1 (0,01 0,08 0,48) (0,00 0,03 0,23) (0,02 0,12 0,52) (0,01 0,09 0,52) (0,02 0,13 0,49) A 2 (0,02 0,10 0,57) (0,00 0,03 0,23) (0,02 0,12 0,52) (0,01 0,10 0,54) (0,02 0,17 0,52) A 3 (0,01 0,06 0,45) (0,00 0,03 0,23) (0,02 0,14 0,52) (0,01 0,10 0,54) (0,02 0,15 0,52) A* A- A 1 3.61 2.56 A 2 3.52 2.77 A 3 3.59 2.66 105 106 CURRICULUM VITAE Name Surname : İpek Nur Aksu Permanent Address : Halk Cad. Gül Sok. Ağaoğlu My World Starland Sitesi D1-1 Blok Daire 126 Batı Ataşehir – İST. Birthplace and Date : Samsun, 1986 Second Language : English Primary School : Mehmetçik İlkokulu-Merzifon Secondary School : Fethiye Kemal Mumcu Anadolu Lisesi-Ankara High School : Fethiye Kemal Mumcu Anadolu Lisesi-Ankara Bachelor School : Bahçeşehir University, Industrial Engineering Graduate School : Bahçeşehir University Institute Name : Graduate School of Natural and Applied Sciences Program : Industrial Engineering Publications : - Work Life : Bahçeşehir University, Faculty of Engineering, Industrial Engineering Department, Teaching Assistant (2010, 2012) 107 EXCEL CALCULATIONS Knowledge 1,00 1,00 1,00 0,11 0,14 0,20 0,14 0,20 0,33 Skills 5,00 7,00 9,00 1,00 1,00 1,00 1,00 1,00 3,00 Abilities 3,00 5,00 7,00 0,33 1,00 1,00 1,00 1,00 1,00 Knowledge 1,00 1,00 1,00 0,14 0,20 0,33 0,20 0,33 1,00 Skills 3,00 5,00 7,00 1,00 1,00 1,00 1,00 1,00 3,00 Abilities 1,00 3,00 5,00 0,33 1,00 1,00 1,00 1,00 1,00 Knowledge 1,00 1,00 1,00 0,12 0,17 0,26 0,17 0,26 0,57 0,27 0,35 0,53 r 1 Skills 3,87 5,92 7,94 1,00 1,00 1,00 1,00 1,00 3,00 1,57 1,81 2,88 r 2 Abilities 1,73 3,87 5,92 0,33 1,00 1,00 1,00 1,00 1,00 0,83 1,57 1,81 r 3 0,05 0,09 0,20 w 1 0,30 0,48 1,08 w 2 0,16 0,42 0,68 w 3 0,10 Knowledge 0,54 Skills 0,36 Abilities r i w i w r Abilities Skills Abilities Knowledge Skills Abilities Fuzzy Decision Matrix by 1st Decision Maker Fuzzy Decision Matrix by 2nd Decision Maker Fuzzy Aggregated Decision Matrix Knowledge Skills Knowledge Occupational Knowledge 1,00 1,00 1,00 7,00 9,00 9,00 0,14 0,20 0,33 3,00 5,00 7,00 Foreign Language Knowledge 0,11 0,11 0,14 1,00 1,00 1,00 0,11 0,14 0,20 0,14 0,20 0,33 Graduated School 3,00 5,00 7,00 5,00 7,00 9,00 1,00 1,00 1,00 5,00 7,00 9,00 Academic Publishing 0,14 0,20 0,33 3,00 5,00 7,00 0,11 0,14 0,20 1,00 1,00 1,00 Occupational Knowledge 1,00 1,00 1,00 3,00 5,00 7,00 3,00 5,00 7,00 3,00 5,00 7,00 Foreign Language Knowledge 0,14 0,20 0,33 1,00 1,00 1,00 0,14 0,20 0,33 0,20 0,33 1,00 Graduated School 0,14 0,20 0,33 3,00 5,00 7,00 1,00 1,00 1,00 1,00 3,00 5,00 Academic Publishing 0,14 0,20 0,33 1,00 3,00 5,00 0,20 0,33 1,00 1,00 1,00 1,00 Occupational Knowledge 1,00 1,00 1,00 4,58 6,71 7,94 0,65 1,00 1,52 3,00 5,00 7,00 1,73 2,41 3,03 r1 Foreign Language Knowledge 0,12 0,15 0,21 1,00 1,00 1,00 0,12 0,17 0,26 0,17 0,26 0,57 0,23 0,28 0,42 r2 Graduated School 0,65 1,00 1,52 3,87 5,92 7,94 1,00 1,00 1,00 2,24 4,58 6,71 1,54 2,28 3,00 r3 Academic Publishing 0,14 0,20 0,33 1,73 3,87 5,92 0,15 0,21 0,45 1,00 1,00 1,00 0,44 0,64 0,97 r4 0,23 0,43 0,77 w 1 0,03 0,05 0,11 w 2 0,21 0,41 0,76 w 3 0,06 0,11 0,25 w 4 0,42 Occupational Knowledge 0,06 Foreign Language Knowledge 0,40 Graduated School 0,12 Academic Publishing Knowledge g g g Knowledge Graduated School Publishing Academic ri w i w r Fuzzy Decision Matrix by 1st Decision Maker Fuzzy Decision Matrix by 2nd Decision Maker Fuzzy Aggregated Decision Matrix Occupational Foreign Language Graduated School Academic Occupational Foreign Language Graduated School Basic Skills 1,00 1,00 1,00 1,00 3,00 5,00 3,00 5,00 7,00 0,14 0,20 0,33 1,00 1,00 3,00 0,11 0,14 0,20 0,14 0,20 0,33 0,20 0,33 1,00 Complex Problem Solving Skills 0,20 0,33 1,00 1,00 1,00 1,00 5,00 7,00 9,00 0,14 0,20 0,33 3,00 5,00 7,00 0,11 0,14 0,20 0,14 0,20 0,33 1,00 1,00 3,00 System Skills 0,14 0,20 0,33 0,11 0,14 0,20 1,00 1,00 1,00 0,11 0,14 0,20 0,20 0,33 1,00 0,11 0,14 0,20 0,14 0,20 0,33 0,11 0,14 0,20 Experience 3,00 5,00 7,00 3,00 5,00 7,00 5,00 7,00 9,00 1,00 1,00 1,00 1,00 1,00 3,00 0,11 0,14 0,20 0,14 0,20 0,33 3,00 5,00 7,00 Number of Case 0,33 1,00 1,00 0,14 0,20 0,33 1,00 3,00 5,00 0,33 1,00 1,00 1,00 1,00 1,00 0,14 0,20 0,33 0,20 0,33 1,00 0,14 0,20 0,33 Success rate of Cases 5,00 7,00 9,00 5,00 7,00 9,00 7,00 9,00 9,00 5,00 7,00 9,00 3,00 5,00 7,00 1,00 1,00 1,00 0,11 0,14 0,20 1,00 3,00 5,00 Stabilisation 3,00 5,00 7,00 3,00 5,00 7,00 3,00 5,00 7,00 3,00 5,00 7,00 1,00 3,00 5,00 5,00 7,00 9,00 1,00 1,00 1,00 3,00 5,00 7,00 Reference 1,00 3,00 5,00 0,33 1,00 1,00 5,00 7,00 9,00 0,14 0,20 0,33 3,00 5,00 7,00 0,20 0,33 1,00 0,14 0,20 0,33 1,00 1,00 1,00 Basic Skills 1,00 1,00 1,00 0,14 0,20 0,33 0,20 0,33 1,00 0,11 0,14 0,20 0,11 0,14 0,20 0,11 0,14 0,20 0,11 0,14 0,20 0,20 0,33 1,00 Complex Problem Solving Skills 3,00 5,00 7,00 1,00 1,00 1,00 3,00 5,00 7,00 1,00 3,00 5,00 1,00 3,00 5,00 1,00 1,00 3,00 1,00 3,00 5,00 1,00 3,00 5,00 System Skills 1,00 3,00 5,00 0,14 0,20 0,33 1,00 1,00 1,00 0,20 0,33 1,00 0,14 0,20 0,33 0,14 0,20 0,33 0,14 0,20 0,33 0,20 0,33 1,00 Experience 5,00 7,00 9,00 0,20 0,33 1,00 1,00 3,00 5,00 1,00 1,00 1,00 1,00 1,00 3,00 0,20 0,33 1,00 1,00 3,00 5,00 1,00 3,00 5,00 Number of Case 5,00 7,00 9,00 0,20 0,33 1,00 3,00 5,00 7,00 0,33 1,00 1,00 1,00 1,00 1,00 0,11 0,14 0,20 3,00 5,00 7,00 3,00 5,00 7,00 Success rate of Cases 5,00 7,00 9,00 0,33 1,00 1,00 3,00 5,00 7,00 1,00 3,00 5,00 5,00 7,00 9,00 1,00 1,00 1,00 3,00 5,00 7,00 3,00 5,00 7,00 Stabilisation 5,00 7,00 9,00 0,20 0,33 1,00 3,00 5,00 7,00 0,20 0,33 1,00 0,14 0,20 0,33 0,14 0,20 0,33 1,00 1,00 1,00 1,00 3,00 5,00 Reference 1,00 3,00 5,00 0,20 0,33 1,00 1,00 3,00 5,00 0,20 0,33 1,00 0,14 0,20 0,33 0,14 0,20 0,33 0,20 0,33 1,00 1,00 1,00 1,00 Basic Skills 1,00 1,00 1,00 0,37 0,77 1,28 0,77 1,28 2,65 0,12 0,17 0,26 0,33 0,37 0,77 0,11 0,14 0,20 0,12 0,17 0,26 0,20 0,33 1,00 0,23 0,34 0,62 r 1 Complex Problem Solving Skills 0,77 1,28 2,65 1,00 1,00 1,00 3,87 5,92 7,94 0,37 0,77 1,28 1,73 3,87 5,92 0,33 0,37 0,77 0,37 0,77 1,28 1,00 1,73 3,87 0,82 1,42 2,50 r 2 System Skills 0,37 0,77 1,28 0,12 0,17 0,26 1,00 1,00 1,00 0,15 0,21 0,45 0,17 0,26 0,57 0,12 0,17 0,26 0,14 0,20 0,33 0,15 0,21 0,45 0,16 0,24 0,44 r 3 Experience 3,87 5,92 7,94 0,77 1,28 2,65 2,24 4,58 6,71 1,00 1,00 1,00 1,00 1,00 3,00 0,15 0,21 0,45 0,37 0,77 1,28 1,73 3,87 5,92 0,94 1,56 2,83 r 4 Number of Case 1,28 2,65 3,00 0,17 0,26 0,57 1,73 3,87 5,92 0,33 1,00 1,00 1,00 1,00 1,00 0,12 0,17 0,26 0,77 1,28 2,65 0,65 1,00 1,52 0,50 0,92 1,40 r 5 Success rate of Cases 5,00 7,00 9,00 1,28 2,65 3,00 4,58 6,71 7,94 2,24 4,58 6,71 3,87 5,92 7,94 1,00 1,00 1,00 0,57 0,84 1,18 1,73 3,87 5,92 2,21 3,77 5,02 r 6 Stabilisation 3,87 5,92 7,94 0,77 1,28 2,65 3,00 5,00 7,00 0,77 1,28 2,65 0,37 0,77 1,28 0,84 1,18 1,72 1,00 1,00 1,00 1,73 3,87 5,92 1,21 2,09 3,39 r 7 Reference 1,00 3,00 5,00 0,26 0,57 1,00 2,24 4,58 6,71 0,17 0,26 0,57 0,65 1,00 1,52 0,17 0,26 0,57 0,17 0,26 0,57 1,00 1,00 1,00 0,40 0,75 1,38 r 8 0,01 0,03 0,10 w1 0,05 0,13 0,39 w2 0,01 0,02 0,07 w3 0,05 0,14 0,44 w4 0,03 0,08 0,22 w5 0,13 0,34 0,78 w6 0,07 0,19 0,52 w7 0,02 0,07 0,21 w8 0,03 Basic Skills 0,14 Complex Problem Solving Skills 0,02 System Skills 0,15 Experience 0,08 Number of Case 0,30 Success rate of Cases 0,19 Stabilisation 0,07 Reference Number of CaseBasic Skills Complex Problem System Skills Experience r i wi wr Stabilisation ReferenceSuccess rate of Stabilisation Reference Basic Skills Complex Problem System Skills Experience Number of Case Success rate of Stabilisation Reference Fuzzy Decision Matrix by 1st Decision Matrix Fuzzy Decision Matrix by 2nd Decision Matrix Fuzzy Aggregated Decision Matrix Basic Skills Complex Problem System Skills Experience Number of Case Success rate of Psychomotor Abilities 1,00 1,00 1,00 0,20 0,33 1,00 0,14 0,20 0,33 Cognitive Abilities 1,00 3,00 5,00 1,00 1,00 1,00 0,20 0,33 1,00 Managerial Competence 3,00 5,00 7,00 1,00 3,00 5,00 1,00 1,00 1,00 Psychomotor Abilities 1,00 1,00 1,00 1,00 3,00 5,00 3,00 5,00 7,00 Cognitive Abilities 0,20 0,33 1,00 1,00 1,00 1,00 1,00 1,00 3,00 Managerial Competence 0,14 0,20 0,33 0,33 1,00 1,00 1,00 1,00 1,00 Psychomotor Abilities 1,00 1,00 1,00 0,45 0,99 2,24 0,65 1,00 1,52 0,66 1,00 1,50 r 1 Cognitive Abilities 0,45 0,99 2,24 1,00 1,00 1,00 0,45 0,57 1,73 0,58 0,83 1,57 r 2 Managerial Competence 0,65 1,00 1,52 0,57 1,73 2,24 1,00 1,00 1,00 0,72 1,20 1,50 r 3 0,14 0,33 0,76 w 1 0,13 0,27 0,80 w 2 0,16 0,40 0,76 w 3 0,33 Psychomotor Abilities 0,32 Cognitive Abilities 0,35 Managerial Competence w i w r Fuzzy Decision Matrix by 1st Decision Matrix Fuzzy Aggregated Decision Matrix Psychomotor Cognitive Abilities Managerial Psychomotor Cognitive Abilities Managerial Cognitive Abilities Managerial Fuzzy Decision Matrix by 2nd Decision Maker r iPsychomotor Occupational Knowledge 0,23 0,43 0,77 0,05 0,09 0,20 0,01 0,04 0,15 Foreign Language Knowledge 0,03 0,05 0,11 0,05 0,09 0,20 0,00 0,00 0,02 Graduated School 0,21 0,41 0,76 0,05 0,09 0,20 0,01 0,04 0,15 Academic Publishing 0,06 0,11 0,25 0,05 0,09 0,20 0,00 0,01 0,05 Basic Skills 0,01 0,03 0,10 0,30 0,54 1,08 0,00 0,02 0,10 Complex Problem Solving Skills 0,05 0,13 0,39 0,30 0,54 1,08 0,01 0,07 0,42 System Skills 0,01 0,02 0,07 0,30 0,54 1,08 0,00 0,01 0,07 Experience 0,05 0,14 0,44 0,30 0,54 1,08 0,02 0,08 0,47 Number of Case 0,03 0,08 0,22 0,30 0,54 1,08 0,01 0,04 0,23 Success rate of Cases 0,13 0,34 0,78 0,30 0,54 1,08 0,04 0,18 0,84 Stabilisation 0,07 0,19 0,52 0,30 0,54 1,08 0,02 0,10 0,57 Reference 0,02 0,07 0,21 0,30 0,54 1,08 0,01 0,04 0,23 Psychomotor Abilities 0,14 0,33 0,76 0,16 0,42 0,68 0,02 0,14 0,52 Cognitive Abilities 0,13 0,27 0,80 0,16 0,42 0,68 0,02 0,12 0,54 Managerial Competence 0,16 0,40 0,76 0,16 0,42 0,68 0,03 0,17 0,52 Occupational Knowledge Foreign Language Knowledge Graduated School A 1 5,00 7,00 9,00 3,00 5,00 7,00 A 1 3,00 5,00 7,00 7,00 9,00 10,00 A 1 3,00 5,00 7,00 5,00 7,00 9,00 A 2 9,00 10,00 10,00 9,00 10,00 10,00 A 2 7,00 9,00 10,00 9,00 10,00 10,00 A 2 9,00 10,00 10,00 7,00 9,00 10,00 A 3 7,00 9,00 10,00 5,00 7,00 9,00 A 3 3,00 5,00 7,00 3,00 5,00 7,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 Academic Publishing Basic Skills Complex Problem Solving Skills A 1 7,00 9,00 10,00 7,00 9,00 10,00 A 1 3,00 5,00 7,00 3,00 5,00 7,00 A 1 5,00 7,00 9,00 9,00 10,00 10,00 A 2 9,00 10,00 10,00 9,00 10,00 10,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 2 7,00 9,00 10,00 5,00 7,00 9,00 A 3 3,00 5,00 7,00 1,00 3,00 5,00 A 3 9,00 10,00 10,00 7,00 9,00 10,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 System Skills Experience Number of Case A 1 7,00 9,00 10,00 7,00 9,00 10,00 A 1 3,00 5,00 7,00 5,00 7,00 9,00 A 1 3,00 5,00 7,00 3,00 5,00 7,00 A 2 5,00 7,00 9,00 7,00 9,00 10,00 A 2 9,00 10,00 10,00 9,00 10,00 10,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 3 5,00 7,00 9,00 3,00 5,00 7,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 A 3 5,00 7,00 9,00 5,00 7,00 9,00 Success rate of Cases Stabilisation Reference A 1 7,00 9,00 10,00 7,00 9,00 10,00 A 1 3,00 5,00 7,00 9,00 10,00 10,00 A 1 7,00 9,00 10,00 7,00 9,00 10,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 2 9,00 10,00 10,00 7,00 9,00 10,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 3 5,00 7,00 9,00 5,00 7,00 9,00 A 3 3,00 5,00 7,00 5,00 7,00 9,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 Psychomotor Abilities Cognitive Abilities Managerial Competence A 1 7,00 9,00 10,00 7,00 9,00 10,00 A 1 7,00 9,00 10,00 5,00 7,00 9,00 A 1 7,00 9,00 10,00 5,00 7,00 9,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 2 7,00 9,00 10,00 7,00 9,00 10,00 A 2 9,00 10,00 10,00 9,00 10,00 10,00 A 3 9,00 10,00 10,00 9,00 10,00 10,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 A 3 7,00 9,00 10,00 7,00 9,00 10,00 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM 1st DM 2nd DM C27 A 1 5,00 7,00 9,00 3,00 5,00 7,00 3,00 5,00 7,00 7,00 9,00 10,00 3,00 5,00 7,00 5,00 7,00 9,00 7,00 9,00 10,00 3,00 5,00 7,00 3,00 5,00 7,00 7,00 9,00 10,00 3,00 5,00 7,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 A 2 9,00 10,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 5,00 7,00 9,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 A 3 7,00 9,00 10,00 3,00 5,00 7,00 7,00 9,00 10,00 3,00 5,00 7,00 9,00 10,00 10,00 7,00 9,00 10,00 5,00 7,00 9,00 7,00 9,00 10,00 5,00 7,00 9,00 5,00 7,00 9,00 3,00 5,00 7,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 C27 A 1 3,00 5,00 7,00 7,00 9,00 10,00 5,00 7,00 9,00 7,00 9,00 10,00 3,00 5,00 7,00 9,00 10,00 10,00 7,00 9,00 10,00 5,00 7,00 9,00 3,00 5,00 7,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 5,00 7,00 9,00 5,00 7,00 9,00 A 2 9,00 10,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 5,00 7,00 9,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 A 3 5,00 7,00 9,00 3,00 5,00 7,00 7,00 9,00 10,00 1,00 3,00 5,00 7,00 9,00 10,00 7,00 9,00 10,00 3,00 5,00 7,00 7,00 9,00 10,00 5,00 7,00 9,00 5,00 7,00 9,00 5,00 7,00 9,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 C27 A 1 4,00 6,00 8,00 5,00 7,00 8,50 4,00 6,00 8,00 7,00 9,00 10,00 3,00 5,00 7,00 7,00 8,50 9,50 7,00 9,00 10,00 4,00 6,00 8,00 3,00 5,00 7,00 7,00 9,00 10,00 6,00 7,50 8,50 7,00 9,00 10,00 7,00 9,00 10,00 6,00 8,00 9,50 6,00 8,00 9,50 A 2 9,00 10,00 10,00 8,00 9,50 10,00 8,00 9,50 10,00 9,00 10,00 10,00 7,00 9,00 10,00 6,00 8,00 9,50 6,00 8,00 9,50 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 8,00 9,50 10,00 7,00 9,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 9,00 10,00 10,00 A 3 6,00 8,00 9,50 3,00 5,00 7,00 7,00 9,00 10,00 2,00 4,00 6,00 8,00 9,50 10,00 7,00 9,00 10,00 4,00 6,00 8,00 7,00 9,00 10,00 5,00 7,00 9,00 5,00 7,00 9,00 4,00 6,00 8,00 7,00 9,00 10,00 9,00 10,00 10,00 7,00 9,00 10,00 7,00 9,00 10,00 C27 A 1 0,40 0,60 0,80 0,50 0,70 0,85 0,40 0,60 0,80 0,70 0,90 1,00 0,30 0,50 0,70 0,70 0,85 0,95 0,70 0,90 1,00 0,40 0,60 0,80 0,30 0,50 0,70 0,70 0,90 1,00 0,60 0,75 0,85 0,70 0,90 1,00 0,70 0,90 1,00 0,60 0,80 0,95 0,60 0,80 0,95 A 2 0,90 1,00 1,00 0,80 0,95 1,00 0,80 0,95 1,00 0,90 1,00 1,00 0,70 0,90 1,00 0,60 0,80 0,95 0,60 0,80 0,95 0,90 1,00 1,00 0,70 0,90 1,00 0,70 0,90 1,00 0,80 0,95 1,00 0,70 0,90 1,00 0,70 0,90 1,00 0,70 0,90 1,00 0,90 1,00 1,00 A 3 0,60 0,80 0,95 0,30 0,50 0,70 0,70 0,90 1,00 0,20 0,40 0,60 0,80 0,95 1,00 0,70 0,90 1,00 0,40 0,60 0,80 0,70 0,90 1,00 0,50 0,70 0,90 0,50 0,70 0,90 0,40 0,60 0,80 0,70 0,90 1,00 0,90 1,00 1,00 0,70 0,90 1,00 0,70 0,90 1,00 C 11 0,01 0,04 0,15 C 12 0,00 0,00 0,02 C 13 0,01 0,04 0,15 C 14 0,00 0,01 0,05 C 21 0,00 0,02 0,10 C 22 0,01 0,07 0,42 C 23 0,00 0,01 0,07 C 24 0,02 0,08 0,47 C 25 0,01 0,04 0,23 C 26 0,04 0,18 0,84 C 27 0,02 0,10 0,57 C 28 0,01 0,04 0,23 C 31 0,02 0,14 0,52 C 32 0,02 0,12 0,54 C 33 0,03 0,17 0,52 C27 A 1 0,00 0,02 0,12 0,00 0,00 0,02 0,00 0,02 0,12 0,00 0,01 0,05 0,00 0,01 0,07 0,01 0,06 0,40 0,00 0,01 0,07 0,01 0,05 0,38 0,00 0,02 0,16 0,03 0,17 0,84 0,01 0,08 0,48 0,00 0,03 0,23 0,02 0,12 0,52 0,01 0,09 0,52 0,02 0,13 0,49 A 2 0,01 0,04 0,15 0,00 0,00 0,02 0,01 0,03 0,15 0,00 0,01 0,05 0,00 0,01 0,10 0,01 0,06 0,40 0,00 0,01 0,07 0,01 0,08 0,47 0,01 0,04 0,23 0,03 0,17 0,84 0,02 0,10 0,57 0,00 0,03 0,23 0,02 0,12 0,52 0,01 0,10 0,54 0,02 0,17 0,52 A 3 0,01 0,03 0,15 0,00 0,00 0,02 0,01 0,03 0,15 0,00 0,00 0,03 0,00 0,02 0,10 0,01 0,06 0,42 0,00 0,01 0,06 0,01 0,07 0,47 0,00 0,03 0,21 0,02 0,13 0,75 0,01 0,06 0,45 0,00 0,03 0,23 0,02 0,14 0,52 0,01 0,10 0,54 0,02 0,15 0,52 A * 0,15 0,15 0,15 0,02 0,02 0,02 0,15 0,15 0,15 0,05 0,05 0,05 0,10 0,10 0,10 0,40 0,40 0,40 0,07 0,07 0,07 0,47 0,47 0,47 0,23 0,23 0,23 0,84 0,84 0,84 0,57 0,57 0,57 0,23 0,23 0,23 0,52 0,52 0,52 0,54 0,54 0,54 0,52 0,52 0,52 A - 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,01 0,01 0,01 0,00 0,00 0,00 0,01 0,01 0,01 0,00 0,00 0,00 0,02 0,02 0,02 0,01 0,01 0,01 0,00 0,00 0,00 0,02 0,02 0,02 0,01 0,01 0,01 0,02 0,02 0,02 C 11 C 12 C 13 C 14 C 21 C 22 C 23 C 24 C 25 C 26 C 27 C 28 C 31 C 32 C 33 Sum A 1 0,11 0,01 0,11 0,04 0,08 0,30 0,05 0,37 0,18 0,61 0,43 0,17 0,37 0,40 0,37 3,61 A 2 0,10 0,01 0,11 0,04 0,07 0,30 0,05 0,35 0,17 0,61 0,42 0,17 0,37 0,39 0,35 3,52 A 3 0,11 0,02 0,11 0,04 0,07 0,30 0,05 0,35 0,17 0,63 0,44 0,17 0,36 0,39 0,36 3,59 C 11 C 12 C 13 C 14 C 21 C 22 C 23 C 24 C 25 C 26 C 27 C 28 C 31 C 32 C 33 S um A 1 0,07 0,01 0,07 0,03 0,04 0,23 0,04 0,21 0,10 0,48 0,27 0,13 0,29 0,30 0,28 2,56 A 2 0,05 0,01 0,09 0,03 0,06 0,23 0,04 0,27 0,14 0,48 0,32 0,13 0,29 0,31 0,30 2,77 A 3 0,09 0,01 0,09 0,02 0,06 0,24 0,03 0,27 0,12 0,43 0,26 0,13 0,30 0,31 0,30 2,66 A 1 0,42 A 2 0,44 A 3 0,43 C33 Fuzzy Weighted Matrix C24 C25 C26 C28 C31C22 Distance from FPIS Distance from FNIS The closeness coefficient of each alternative C28 C32 C32 C33 Weighted Normalized Fuzzy Decision Matrix C11 C12 C13 C14 C21 C23 C23 C24 C25 C33 Normalized Fuzzy Decision Matrix C31C11 C12 C13 C14 C21 C22 C26 C26 C28 C31 C32 Aggregated Fuzzy Decision Matrix C11 C12 C13 C14 C21 C22 C23 C24 C25 C32 C33 The ratings of the three candidates by 1st decision maker under all criteria The ratings of the three candidates by 2nd decision maker under all criteria C28 C31 C32 C33 C21 C22 C28 C31C11 C12 C13 C14 C25 C26 C23 C24 C25 C26 C21 C22 C23 C24C11 C12 C13 C14