Copernican Journal of Finance & Accounting e-ISSN 2300-3065 p-ISSN 2300-12402016, volume 5, issue 1 Date of submission: May 22, 2016; date of acceptance: June 11, 2016. * Contact information: nkerdoga@anadolu.edu.tr, Anadolu University, Faculty of Busi- ness, Department of Business Administration, Eskişehir/Turkey, phone: +902223350580 (2543). ** Contact information: saltinirmak@anadolu.edu.tr, Anadolu University, Eskişehir Vo- cational High School, Department of Finance, Eskişehir/Turkey, phone: +902223350580 (3138). *** Contact information: ckaramasa@anadolu.edu.tr, Anadolu University, Faculty of Busi- ness, Department of Business Administration, Eskişehir/Turkey, phone: +902223350580 (2554). Erdoğan N. K., Altınırmak S., & Karamaşa Ç. (2016). Comparison of multi criteria decision making (MCDM) methods with respect to performance of food firms listed in BIST. Copernican Journal of Finance & Accounting, 5(1), 67–90. http://dx.doi.org/10.12775/CJFA.2016.004 Namık kemal erdoğaN* Anadolu University serpil altinirMak** Anadolu University Çağlar karamaşa*** Anadolu University coMparison of Multi criteria decision Making (McdM) Methods with respect to perforMance of food firMs listed in bist Keywords: performance analysis, fuzzy ranking, TOPSIS, VIKOR, ELECTRE. J E L Classification: C44, D81, L25. Abstract: Analyzing firms’ performance appropriately is core topic for decision ma- kers working in financial sector under the conditions of imprecise and incomplete in- Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa68 formation. Purpose of this study is to assess firms’ performance by taking financial ra- tios and financial experts’ into the account. Therefore firstly weights of criteria and sub criteria related to financial ratios are obtained by using one of the fuzzy ranking me- thods namely Buckley’s Column Geometric Mean Method. Following to this firms’ final rankings are determined by means of TOPSIS, VIKOR and ELECTRE methods. Also ran- king performance of these three methods is interpreted. According to this purpose fi- nancial ratios of twenty one food firms listed in BIST for four years period (2011–2014) are acquired and analyzed via these methods.  Introduction Performance can be defined as efficiency in production or effectiveness in ser- vice. It is important to determine performance for firms’ future condition. For that reason firms’ performance should be measured. Neely et al. (1995) de- scribed the performance measurement as determination process of an activ- ity’s efficiency and effectiveness quantity (Yüreğir, Nakıboğlu 2007). Business executives view past decisions’ results and make future investment decisions via financial performance measurement (Uyguntürk, Korkmaz 2012). Finan- cial analysis which can be made by business executives, investors or credit firms is based on establishing relationships between items appeared in finan- cial tables and commenting on this matter. Financial ratios show relationships between financial table items mathe- matically (İç, Tekin,Pamukoğlu,Yıldırım 2015). Firms’ strengths and weakness- es in terms of liquidity, growth and profitability can be revealed by financial ratios. Firms’ year based changes and sector based performance comparisons are made with the aim of financial ratios (Uyguntürk, Korkmaz 2012). Finan- cial ratios are chosen according to financial sector applications and finance lit- erature. Basically financial ratios are classified into four group namely liquid- ity, financial structure, operating and profitability ratios. Firms’ ability to pay short-term debts are determined via liquidity ratios. Currency ratio, acid test ratio and cash ratio are included in first group. Financial structure ratios are used for determining the firm’s outsourcing level. Leverage ratio denoted as total debts/total assets is considered in second group and it is possible to detect the percentage of assets subsidized by debts in case of assets selling (Dumanoğlu 2010). Operating ratios are used for exhibit- ing the efficient usage level of firms’ assets. Asset turnover ratio denoted as net sales/total assets is considered in third group. Profitability ratios are used for measuring the earning power of firms’ after activities fulfilled. Ratios namely ComParison of multi CritEria dECision making… 69 net profit/total assets, net profit/capital and net profit/net sales are included in last group. Financial ratios used in this study are showed in Table 1. Table 1. Financial Ratios Financial Ratio Groups Ratios Explanation Liquidity Ratios Currency Ratio Current Assets/Short Term Debts Acid Test Ratio (Currents Assets- Stocks)/Short Term Debts Cash Ratio (Liquid Assets + Securities)/ Short Term Debts Financial Structure Ratios Leverage Ratio Total Debts/Total Assets Operating Ratios Asset Turnover Ratio Net Sales/ Total Assets Profitability Ratios Net Profit/Total Assets Net Profit/Total Assets Net Profit/Capital Net Profit/Capital Net Profit/Net Sales Net Profit/Net Sales S o u r c e : Tayyar, Akcanlı, Genç, Eram 2014. Purpose of this study is to assess the properties of different Multi Criteria Decision Making (MCDM) methods and compare the results of them in terms of food firms’ performance assessment by taking financial ratios and financial experts’ view into the account. For this reason firstly local and global weights of criteria and sub- criteria related to financial ratios are obtained by using one of the fuzzy ranking methods namely Buckley’s Column Geometric Mean Meth- od. Following to this firms’ final rankings are determined by means of TOPSIS, VIKOR and ELECTRE methods. Data sets for this study are financial ratios of twenty one food firms listed in BIST. Literature Review First financial analysis studies assessed via objective methods were made by Altman (1968). Altman acquired a discriminant function namely ʺz score mod- el” by using financial ratios. Difficulties encountered in data entering and ac- quiring caused the method based on past years data to be developed. Usage of MCDM methods in measuring firms’ financial performance is started to be- come widespread since 1980s (İç et al. 2015). Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa70 Feng and Wang (2000) examined the performance of five airlines operated in Taiwan by means of TOPSIS and concluded the importance of financial indi- cators on the determination of airlines’ performance. Yurdakul and İç (2003) examined the five large scale automobile firm in terms of financial structures and condition in the sector. Performance values for each year are compared with securities’ year-end closing prices and results are found as consistent out of 2001. Mahmoodzadeh, Shahrabi, Pariazar and Zaeri (2007) determined the preference ranking of different projects by the means of fuzzy AHP, TOPSIS and traditional project evaluation methods such as net present value, rate of return, benefit-cost analysis and payback period. Wu, Tzeng and Chen (2009) proposed a fuzzy MCDM approach in order to evaluate banking performanc- es based on Balanced Scorecard (BSC). For this purpose twenty three perfor- mance evaluation indexes were selected for banking performance of BSC by taking into the expert questionnaires. After that FAHP was employed to obtain relative weights of performance evaluation indexes and three MCDM methods (SAW, TOPSIS and VIKOR) were used to rank banking performances. Bülbül and Köse (2011) evaluated the financial performance of food sector on the ba- sis of company and sector via TOPSIS and ELECTRE methods and found con- sistent results. Research Methodology AHP, developed by Saaty (1980), is a decision making mechanism composed of overall goal, criteria and sub criteria (if there are any), and alternatives. AHP methodology can be used for making decisions where choice, prioritization and forecasting are needed. AHP is based on structuring problem and eliciting properties through pairwise comparisons in decision making process (Ishiza- ka, Nemery 2013). By using AHP we can decouple problem into sub problems by evaluating subjectively manner that is transformed into numerical values and ranked on a numerical scale (Bhushan, Rai 2004). Despite these specifications, AHP can not ref lect human thinking style in inaccurate and subjective environment due to unbalanced scale of judgments, inability to adequately handle inherent uncertainty and imprecise pair-wise comparisons. For that reason fuzzy analytic hierarchy process (FAHP) exten- sion of traditional AHP was developed to solve hierarchical fuzzy problems in interval judgment matrix (Kahraman, Cebeci, Ulukan 2003). ComParison of multi CritEria dECision making… 71 Zadeh (1965) firstly proposed a mathematical theory namely fuzzy set in order to overcome vaguness and imprecise condition of human cognitive pro- cesses (Jie, Meng, Cheong 2006). Apart from classical set theory based on bi- nary logic fuzzy set describe actual objects similar to human language (Huang, Ho 2013). A fuzzy set which is extension of crisp one allow partial belonging of element by membership function. Membership values of objects in a fuzzy set range from 0 (nonmembership) to 1 (complete membership). Values between these boundaries are called intermediate membership degrees and show de- gree to which an element belongs to a set (Ertuğrul, Karakaşoğlu 2009). Tri- angular and trapezoidal fuzzy numbers are mostly used in application fields. Triangular fuzzy numbers are used in this study due to computational easiness and representation usefulness. Membership of triangular fuzzy number is defined by three real numbers expressed as (l,m,u) indicating smallest possible value, the most promising val- ue and the largest possible value respectively (Deng 1999). Fuzzy set theory al- low respondents to explain semantic judgments subjectively (Huang, Ho 2013). For this reason Saaty’s 9 point scale is transformed into the fuzzy ratio scale in terms of triangular fuzzy numbers. Ranking fuzzy numbers in imprecise and vagueness environment is one of the essential problems in fuzzy optimization and fuzzy decision making. Fuzzy values are ranked according to the different specifications of fuzzy sets namely centre of attraction, area under the membership degree function and some in- tersection points (Chen, Hwang, Hwang 1992). Various fuzzy ranking methods can be used according to the complexity, sensitivity, easily interpretability of existing problem and type of fuzzy numbers (Kaptanoğlu, Özok 2006). Buck- ley (1985) developed a model to state decision maker’s evaluation on alterna- tives with respect to each criterion by using triangular fuzzy numbers. Steps of Buckley’s Column Geometric Mean method are given as follows: 1. Establishing hierarchical structure and comparing criteria or alternatives via fuzzy scale for constructing pair-wise comparison matrix shown as be- low: degrees and show degree to which an element belongs to a set (Ertuğrul, Karakaşoğlu 2009,704). Triangular and trapezoidal fuzzy numbers are mostly used in application fields. Triangular fuzzy numbers are used in this study due to computational easiness and representation usefulness. Membership of triangular fuzzy number is defined by three real numbers expressed as (l,m,u) indicating smallest possible value, the most promising value and the largest possible value respectively (Deng 1999). Fuzzy set theory allow respondents to explain semantic judgments subjectively (Huang, Ho 2013,985). For this reason Saaty’s 9 point scale is transformed into the fuzzy ratio scale in terms of triangular fuzzy numbers. Ranking fuzzy numbers in imprecise and vagueness environment is one of the essential problems in fuzzy optimization and fuzzy decision making. Fuzzy values are ranked according to the different specifications of fuzzy sets namely centre of attraction, area under the membership degree function and some intersection points (Chen, Hwang, Hwang 1992). Various fuzzy ranking methods can be used according to the complexity, sensitivity, easily interpretability of existing problem and type of fuzzy numbers (Kaptanoğlu, Özok 2006,198). Buckley (1985) developed a model to state decision maker’s evaluation on alternatives with respect to each criterion by using triangular fuzzy numbers. Steps of Buckley’s Column Geometric Mean method are given as follows: 1- Establishing hierarchical structure and comparing criteria or alternatives via fuzzy scale for constructing pair-wise comparison matrix shown as below:               = k mn k 2m k 1m k n2 k 22 k 21 k n1 k 12 k 11 k a~a~a~ a~a~a~ a~a~a~ A ~     (1) 2-Preferences of all decision makers are averaged according to Eq. (2) and new pairwise comparison matrix is obtained as Eq. (3): K a a~ K 1k k ij ij  == (2) (1) Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa72 2. Preferences of all decision makers are averaged according to Eq. (2) and new pairwise comparison matrix is obtained as Eq. (3): (2) degrees and show degree to which an element belongs to a set (Ertuğrul, Karakaşoğlu 2009,704). Triangular and trapezoidal fuzzy numbers are mostly used in application fields. Triangular fuzzy numbers are used in this study due to computational easiness and representation usefulness. Membership of triangular fuzzy number is defined by three real numbers expressed as (l,m,u) indicating smallest possible value, the most promising value and the largest possible value respectively (Deng 1999). Fuzzy set theory allow respondents to explain semantic judgments subjectively (Huang, Ho 2013,985). For this reason Saaty’s 9 point scale is transformed into the fuzzy ratio scale in terms of triangular fuzzy numbers. Ranking fuzzy numbers in imprecise and vagueness environment is one of the essential problems in fuzzy optimization and fuzzy decision making. Fuzzy values are ranked according to the different specifications of fuzzy sets namely centre of attraction, area under the membership degree function and some intersection points (Chen, Hwang, Hwang 1992). Various fuzzy ranking methods can be used according to the complexity, sensitivity, easily interpretability of existing problem and type of fuzzy numbers (Kaptanoğlu, Özok 2006,198). Buckley (1985) developed a model to state decision maker’s evaluation on alternatives with respect to each criterion by using triangular fuzzy numbers. Steps of Buckley’s Column Geometric Mean method are given as follows: 1- Establishing hierarchical structure and comparing criteria or alternatives via fuzzy scale for constructing pair-wise comparison matrix shown as below:               = k mn k 2m k 1m k n2 k 22 k 21 k n1 k 12 k 11 k a~a~a~ a~a~a~ a~a~a~ A ~     (1) 2-Preferences of all decision makers are averaged according to Eq. (2) and new pairwise comparison matrix is obtained as Eq. (3): K a a~ K 1k k ij ij  == (2)               = mn2m1m n22221 n11211 a~a~a~ a~a~a~ a~a~a~ A ~     (3) 3-Geometric mean of each criterion is calculated according to Eq. (4): n/1 n 1j iji a ~z~       = ∏ = , i=1,2,…,m (4) 4-The fuzzy weights )w~( i of each criterion are obtained by finding vector summation of each iz~ , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying iz~ with reverse vector according to Eq. (5): )u,m,l()z~z~z~(z~w~ iii 1 n21ii =⊕⊕⊕⊗= − (5) 5-Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6): 3 uml S iiii ++ = (6) 6-After obtaining crisp weights normalization process is implemented such as Eq. (7):  = = m 1i i i i S S T (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximizes cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreasing utility (Pohekar, Ramachandran 2004,372). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable outputs. On the (3) 3. Geometric mean of each criterion is calculated according to Eq. (4):               = mn2m1m n22221 n11211 a~a~a~ a~a~a~ a~a~a~ A ~     (3) 3-Geometric mean of each criterion is calculated according to Eq. (4): n/1 n 1j iji a ~z~       = ∏ = , i=1,2,…,m (4) 4-The fuzzy weights )w~( i of each criterion are obtained by finding vector summation of each iz~ , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying iz~ with reverse vector according to Eq. (5): )u,m,l()z~z~z~(z~w~ iii 1 n21ii =⊕⊕⊕⊗= − (5) 5-Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6): 3 uml S iiii ++ = (6) 6-After obtaining crisp weights normalization process is implemented such as Eq. (7):  = = m 1i i i i S S T (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximizes cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreasing utility (Pohekar, Ramachandran 2004,372). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable outputs. On the (4) 4. The fuzzy weights of each criterion are obtained by finding vector summa- tion of each , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying with reverse vector according to Eq. (5):               = mn2m1m n22221 n11211 a~a~a~ a~a~a~ a~a~a~ A ~     (3) 3-Geometric mean of each criterion is calculated according to Eq. (4): n/1 n 1j iji a ~z~       = ∏ = , i=1,2,…,m (4) 4-The fuzzy weights )w~( i of each criterion are obtained by finding vector summation of each iz~ , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying iz~ with reverse vector according to Eq. (5): )u,m,l()z~z~z~(z~w~ iii 1 n21ii =⊕⊕⊕⊗= − (5) 5-Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6): 3 uml S iiii ++ = (6) 6-After obtaining crisp weights normalization process is implemented such as Eq. (7):  = = m 1i i i i S S T (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximizes cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreasing utility (Pohekar, Ramachandran 2004,372). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable outputs. On the (5) 5. Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6):               = mn2m1m n22221 n11211 a~a~a~ a~a~a~ a~a~a~ A ~     (3) 3-Geometric mean of each criterion is calculated according to Eq. (4): n/1 n 1j iji a ~z~       = ∏ = , i=1,2,…,m (4) 4-The fuzzy weights )w~( i of each criterion are obtained by finding vector summation of each iz~ , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying iz~ with reverse vector according to Eq. (5): )u,m,l()z~z~z~(z~w~ iii 1 n21ii =⊕⊕⊕⊗= − (5) 5-Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6): 3 uml S iiii ++ = (6) 6-After obtaining crisp weights normalization process is implemented such as Eq. (7):  = = m 1i i i i S S T (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximizes cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreasing utility (Pohekar, Ramachandran 2004,372). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable outputs. On the (6) 6. After obtaining crisp weights normalization process is implemented such as Eq. (7): ComParison of multi CritEria dECision making… 73               = mn2m1m n22221 n11211 a~a~a~ a~a~a~ a~a~a~ A ~     (3) 3-Geometric mean of each criterion is calculated according to Eq. (4): n/1 n 1j iji a ~z~       = ∏ = , i=1,2,…,m (4) 4-The fuzzy weights )w~( i of each criterion are obtained by finding vector summation of each iz~ , acquiring (-1) power of summation vector and replacing in an increasing order, and finally multiplying iz~ with reverse vector according to Eq. (5): )u,m,l()z~z~z~(z~w~ iii 1 n21ii =⊕⊕⊕⊗= − (5) 5-Fuzzy weights composed of fuzzy triangular numbers are transformed into crisp one by using Center of Area defuzzification techniques shown in Eq. (6): 3 uml S iiii ++ = (6) 6-After obtaining crisp weights normalization process is implemented such as Eq. (7):  = = m 1i i i i S S T (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximizes cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreasing utility (Pohekar, Ramachandran 2004,372). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable outputs. On the (7) Hwang and Yoon (1981) assert TOPSIS for analyzing MCDM problems. Basis of this technique is to choose alternative having the shortest euclidean distance from positive ideal solution (PIS) which maximizes benefit and minimizes cost, and the farthest distance from negative ideal solution (NIS) which maximiz- es cost and minimizes benefit (Behzadian, Otaghsara,Yazdani,Ignatius 2012). TOPSIS assumes that each criterion has monotonically increasing or decreas- ing utility (Pohekar, Ramachandran 2004). This technique aims to maximize or minimize each criterion and pairwise comparisons are abstained. In addition to that it does not include complex algorithms and mathematical models, easy to use, requires less input parameters and produces easily understandable out- puts. On the other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1. Forming decision matrix other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) for ranking the alternatives. other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (8) 2. Normalizing decision matrix by other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (9) 3. Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa74 other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (10) 4. Determining positive and negative ideal solution as follows : other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (11) other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cijibijim21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (12) 5. Calculating euclidean distance of alternatives from positive and negative ideal solution as follows: other hand it is difficult to weight attributes and keep consistent judgments in case of additional attributes (Velasquez, Hester 2013,62). Structure of TOPSIS are revealed as follows (Tsaur 2011): 1- Forming decision matrix ( )nxmij )x(X = for ranking the alternatives.                     = nmnj2n1n imij2i1i m2j22221 m1j11211 xxxx xxxx xxxx xxxx X       (8) 2- Normalizing decision matrix by  = = m 1i 2 ij ij ij w w r n,,2,1i = m,,2,1j = (9) 3- Weighting normalized decision matrix by multiplying normalized decision matrix and its’ weights. jijij w.rv = n,,2,1i = m,,2,1j = (10) 4- Determining positive and negative ideal solution as follows : { } ( ) ( ){ }cij i bij i * m * 2 * 1 * jvmin,jvmaxv,,v,vAPIS ΩΩ ∈∈===  (11) { } ( ) ( ){ }cij i bij i m21 jvmax,jvminv,,v,vANIS ΩΩ ∈∈=== −−−−  (12) 5- Calculating euclidean distance of alternatives from positive and negative ideal solution as follows:  = −= m 1j 2* jij * i )vv(d n,,2,1i = (13) (13)  = −− −= m 1j 2 jiji )vv(d n,,2,1i = (14) 6- Calculating relative closeness ( iRC ) of each alternative to ideal solution as below: * ii i i dd d RC + = − − n,,2,1i = [ ]1,0RCi ∈ (15) 7- Ranking alternatives according to their iRC values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating compromised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conflicting criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solution is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal solution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are selected, ranked and compared by utilizing cost or benefit based criteria. In evaluation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Compromised solution should be accepted in order to overcome conflict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relationship between benefit and each criteria function for decision maker. d) Alternatives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f) Decision makers are responsible for approving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best ( *af ) and the worst ( − af ) values for each evaluation criteria are identified. If evaluation criteria (b=1,2,…,n) is based on benefit ; aba * b xmaxf = abab xminf = − (16) (14) 6. Calculating relative closeness ( RCi ) of each alternative to ideal solution as be- low:  = −− −= m 1j 2 jiji )vv(d n,,2,1i = (14) 6- Calculating relative closeness ( iRC ) of each alternative to ideal solution as below: * ii i i dd d RC + = − − n,,2,1i = [ ]1,0RCi ∈ (15) 7- Ranking alternatives according to their iRC values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating compromised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conflicting criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solution is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal solution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are selected, ranked and compared by utilizing cost or benefit based criteria. In evaluation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Compromised solution should be accepted in order to overcome conflict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relationship between benefit and each criteria function for decision maker. d) Alternatives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f) Decision makers are responsible for approving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best ( *af ) and the worst ( − af ) values for each evaluation criteria are identified. If evaluation criteria (b=1,2,…,n) is based on benefit ; aba * b xmaxf = abab xminf = − (16) (15) 7. Ranking alternatives according to their RCi values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating com- promised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conf lict- ing criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solu- tion is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal so- ComParison of multi CritEria dECision making… 75 lution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are se- lected, ranked and compared by utilizing cost or benefit based criteria. In eval- uation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Com- promised solution should be accepted in order to overcome conf lict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relation- ship between benefit and each criteria function for decision maker. d) Alterna- tives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f ) Decision makers are responsible for ap- proving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best  = −− −= m 1j 2 jiji )vv(d n,,2,1i = (14) 6- Calculating relative closeness ( iRC ) of each alternative to ideal solution as below: * ii i i dd d RC + = − − n,,2,1i = [ ]1,0RCi ∈ (15) 7- Ranking alternatives according to their iRC values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating compromised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conflicting criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solution is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal solution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are selected, ranked and compared by utilizing cost or benefit based criteria. In evaluation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Compromised solution should be accepted in order to overcome conflict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relationship between benefit and each criteria function for decision maker. d) Alternatives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f) Decision makers are responsible for approving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best ( *af ) and the worst ( − af ) values for each evaluation criteria are identified. If evaluation criteria (b=1,2,…,n) is based on benefit ; aba * b xmaxf = abab xminf = − (16) and the worst  = −− −= m 1j 2 jiji )vv(d n,,2,1i = (14) 6- Calculating relative closeness ( iRC ) of each alternative to ideal solution as below: * ii i i dd d RC + = − − n,,2,1i = [ ]1,0RCi ∈ (15) 7- Ranking alternatives according to their iRC values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating compromised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conflicting criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solution is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal solution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are selected, ranked and compared by utilizing cost or benefit based criteria. In evaluation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Compromised solution should be accepted in order to overcome conflict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relationship between benefit and each criteria function for decision maker. d) Alternatives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f) Decision makers are responsible for approving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best ( *af ) and the worst ( − af ) values for each evaluation criteria are identified. If evaluation criteria (b=1,2,…,n) is based on benefit ; aba * b xmaxf = abab xminf = − (16) values for each evaluation criteria are identi- fied. If evaluation criteria (b=1,2,…,n) is based on benefit;  = −− −= m 1j 2 jiji )vv(d n,,2,1i = (14) 6- Calculating relative closeness ( iRC ) of each alternative to ideal solution as below: * ii i i dd d RC + = − − n,,2,1i = [ ]1,0RCi ∈ (15) 7- Ranking alternatives according to their iRC values in descending order from 1 to 0 and choosing the highest one. VIKOR developed by Opricovic (1998), is a MCDM based on creating compromised solution by taking alternatives and criteria into the consideration. Method is oriented for selecting and ranking alternatives in case of conflicting criteria (Büyüközkan, Ruan 2008). Compromised solution is the closest to ideal one. In other words VIKOR based on measure of closeness to ideal solution is multi criteria decision ranking index (Opricovic, Tzeng 2004). In order to obtain solution, closest to ideal one, multi criteria ranking index is generated for alternatives and then compared between the values of closeness to ideal solution (Opricovic, Tzeng 2007). Decision making process of VIKOR starts with problem definition. By this way aim of problem, alternatives, criteria and sub criteria (if needed) that will be evaluated are determined. Alternatives are selected, ranked and compared by utilizing cost or benefit based criteria. In evaluation process all alternatives get related criteria scores. VIKOR method can be used for solving MCDM problems if following conditions are satisfied: a) Compromised solution should be accepted in order to overcome conflict. b) Decision maker is willing to accept the closest solution to ideal one. c) A linear relationship between benefit and each criteria function for decision maker. d) Alternatives should be evaluated in terms of each criteria. e) Preferences of decision makers’ are expressed by weights. f) Decision makers are responsible for approving the final solution (Ertuğrul, Karakaşoğlu 2008). Steps of VIKOR method can be summarized as below: a) Best ( *af ) and the worst ( − af ) values for each evaluation criteria are identified. If evaluation criteria (b=1,2,…,n) is based on benefit ; aba * b xmaxf = abab xminf = − (16) (16) If evaluation criteria (b=1,2,…,n) is based on cost; If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20)     If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into nor- malization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements (xkl) is seen as below; If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) (18) Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa76 After normalization process normalization matrix (S) consisted of elements (Skl) is seen as below; If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) (19) c) Weighted normalized decision matrix (T) is obtained by multiplying crite- ria weights (Wb) and normalized decision matrix elements (Sab). If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) If evaluation criteria (b=1,2,…,n) is based on cost; aba * b xminf = abab xmaxf = − (17) b) In order to make comparisons normalization process is used and by this way normalization matrix is obtained. In normalization process decision matrix (X) composed of k criteria and l alternatives transformed into normalization matrix (S) with same dimensions. Before normalization decision matrix (X) consisted of elements ( klx ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 xxxx xxxx xxxx xxxx X       (18) After normalization process normalization matrix (S) consisted of elements ( kls ) is seen as below;                     = klkb2k1k alab2a1a l2b22221 l1b11211 ssss ssss ssss ssss S       −− − = b * b ab * b ab ff xf s (19) c) Weighted normalized decision matrix (T) is obtained by multiplying criteria weights ( bw ) and normalized decision matrix elements ( abs ).                     = klkb2k1k alab2a1a l2b22221 l1b11211 tttt tttt tttt tttt T       babab w.st = (20) (20) d) Values of Sa (mean group score) and Ra (worst group score) are calculated for each alternative. d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) (21) e) Value of Qa is calculated for each alternative. Values of d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) are used to acquire the value of Qa. Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum re- gret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhigu- ang 2008). ComParison of multi CritEria dECision making… 77 d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) (22) d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) f ) Values of Sa, Ra and Qa are ranked from lower to higher and alternative ha- ving minimum Qa value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to Qa values first (Q(C1)) and second alternative (Q(C2)) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) d) Values of aS (mean group score) and aR (worst group score) are calculated for each alternative.  = −− − = l 1b b * b ab * b ba ff xf wS       − − = − b * b ab * b bba ff xf wmaxR (21) e) Value of aQ is calculated for each alternative. Values of −− R,R,S,S ** are used to acquire the value of aQ . Additionally y parameter showing maximum group benefit states the weight of alternative providing maximum group benefit. On the contrary (1-y) parameter refers to weight of minimum regret. Compromise is reached by majority (y>0.5), consensus (y=0.5) or veto (y<0.5) (Opricovic, Tzeng 2007). Generally y=0.5 is used (Lixin, Ying, Zhiguang 2008). aa * SminS = aa SmaxS = − * * a * * a a RR RR )y1( SS SS yQ − − −+ − − = −− (22) aa * RminR = aa RmaxR = − f) Values of aS , aR and aQ are ranked from lower to higher and alternative having minimum aQ value is controlled by two conditions whether ranking is accurate. These conditions are named acceptable advantage and acceptable stability. Acceptable advantage condition: According to aQ values first (Q( 1C )) and second alternative (Q( 2C )) satisfied significant difference. Calculated threshold value (DQ) depend on alternative number. If the number of alternative is lower than 4 the value of DQ equals to 0.25 (Chen, Wang 2009). DQ)C(Q)C(Q 21 ≥− 1k 1 DQ − = (23) (23) Acceptable stability condition: According to Qa values first alternative (Q(C1)) should get the best score at least one for values of S and R. Unless these two conditions are not satisfied compromised solution set is formed by two ways: 1. If second condition is not satisfied first and second alternatives are accep- ted as compromised solution. 2. If first condition is not satisfied C1, C2, …, Ck alternatives are contained in compromised solution set according to Q (Ck) – Q (C1) ≥ DQ (Opricovic, Tzeng 2004). ELECTRE, which was asserted by Roy (1965), is based on outranking rela- tions between alternatives in terms of criteria by using satisfaction and dis- satisfaction measures namely concordance and discordance indexes. Decision makers can select the best alternative via incorporating and weighting crite- ria in this method (Sevkli 2010). In order to solve decision problems more than Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa78 two criteria ELECTRE methods can be preferred to other ones if at least one of these conditions is satisfied: a) Performances of criteria are expressed stated in different units and decision maker does not want to use complex and diffi- cult common scale. b) The problem does not tolerate a compensation effect. c) If there is requirement to use indifference and preference thresholds such that sum of small differences is decisive apart from insignificant small differences. d) If alternatives are weak interval or any order scale in which it is difficult to compare differences (Ishizaka, Nemery 2013). ELECTRE allows decision mak- ers to avoid compensation and between criteria and any normalization process that can distort original data, also uncertain conditions are being considered. On the other hand these methods require difficult technical parameters which are not easily understandable (Ishizaka, Nemery 2013). Different versions of ELECTRE (II, III, IV etc.) can be used according to the decision problem type. Steps of ELECTRE can be summarized as follows (Yoon, Hwang 1995): 1. Forming decision matrix Acceptable stability condition: According to aQ values first alternative (Q( 1C )) should get the best score at least one for values of S and R. Unless these two conditions are not satisfied compromised solution set is formed by two ways: 1-If second condition is not satisfied first and second alternatives are accepted as compromised solution. 2- If first condition is not satisfied k21 C,,C,C  alternatives are contained in compromised solution set according to DQ)C(Q)C(Q 1k ≥− (Opricovic, Tzeng 2004). ELECTRE, which was asserted by Roy (1965), is based on outranking relations between alternatives in terms of criteria by using satisfaction and dissatisfaction measures namely concordance and discordance indexes. Decision makers can select the best alternative via incorporating and weighting criteria in this method (Sevkli 2010,3396). In order to solve decision problems more than two criteria ELECTRE methods can be preferred to other ones if at least one of these conditions is satisfied: a) Performances of criteria are expressed stated in different units and decision maker does not want to use complex and difficult common scale. b) The problem does not tolerate a compensation effect. c) If there is requirement to use indifference and preference thresholds such that sum of small differences is decisive apart from insignificant small differences. d) If alternatives are weak interval or any order scale in which it is difficult to compare differences (Ishizaka, Nemery 2013, 181). ELECTRE allows decision makers to avoid compensation and between criteria and any normalization process that can distort original data, also uncertain conditions are being considered. On the other hand these methods require difficult technical parameters which are not easily understandable (Ishizaka, Nemery 2013,180-182). Different versions of ELECTRE (II, III, IV etc.) can be used according to the decision problem type. Steps of ELECTRE can be summarized as follows (Yoon, Hwang 1995): 1- Forming decision matrix ( )mxnij)a(A = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria. for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for (24) 2. Forming normalized decision matrix                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for for m (i=1,2, …, m) alterna- tives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for (25) ComParison of multi CritEria dECision making… 79                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for for maximization objective (26)                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for for minimization objective (27) 3. Calculating weighted normalized decision matrix                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for via multiply- ing weight of criterion (wj) by elements of normalized decision matrix (xij).                     = mnmj2m1m inij2i1i n2j22221 n1j11211 aaaa aaaa aaaa aaaa A       (24) 2- Forming normalized decision matrix ( )mxnij)x(X = for m (i=1,2, …, m) alternatives and n (j=1,2, …,n) criteria.                     = mnmj2m1m inij2i1i n2j22221 n1j11211 xxxx xxxx xxxx xxxx X       (25)  = = m 1i 2 ij ij ij a a x for maximization objective (26)  =         = m 1i 2 ij ij ij a 1 a 1 x for minimization objective (27) 3- Calculating weighted normalized decision matrix ( )mxnij)v(V = via multiplying weight of criterion ( jw ) by elements of normalized decision matrix ( ijx ). ijjij x.wv = (28) 4- Determining concordance and discordance sets for each pair of alternatives pA and qA (p,q = 1,2, …, m and qp ≠ ) in case of searched alternatives not being the best one for (28) 4. Determining concordance and discordance sets for each pair of alternatives Ap and Ap (p,q = 1,2, …, m and p ≠ q) in case of searched alternatives not be- ing the best one for all criteria. If alternative Ap is preferred to alternative Aq for all criteria concordance set (C(p,q)) , collection of criteria where Ap is better than or equal to Aq, is formed as below: all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. (29) On the other hand if alternative Ap is worse than Aq for all criteria discord- ance set (D(p,q)), collection Ap of criteria for which is worse than Aq, is formed as below: all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. (30) According to the above formulations Vpj is defined as the weighted normal- ized rating of alternative Ap with regard to jth criterion and Vqj is defined as the weighted normalized rating of alternative Aq with respect to jth criterion. 5. Calculating the concordance (Cp,q) and discordance (Dp,q) indexes shown as follows: all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. (31) Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa80 According to Eq. (31) criteria involved in concordance set (C(p,q)) are rep- resented by j*. all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are rep- resented by j+ 6. Relationships between alternatives are outranked by computing the ave- rages of Cpg and Dpg that is represented by all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. and all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. respectively. Accor- ding to this method alternative of Ap outrank the alternative of Aq if and only all criteria. If alternative pA is preferred to alternative qA for all criteria concordance set (C(p,q)) , collection of criteria where pA is better than or equal to qA , is formed as below: C(p,q) = { }qjpj vvj ≥ (29) On the other hand if alternative pA is worse than qA for all criteria discordance set (D(p,q)), collection of criteria for which pA is worse than qA , is formed as below: D(p,q) = { }qjpj vvj < (30) According to the above formulations pjv is defined as the weighted normalized rating of alternative pA with regard to jth criterion and qjv is defined as the weighted normalized rating of alternative qA with respect to jth criterion. 5- Calculating the concordance ( pqC ) and discordance ( pqD ) indexes shown as follows: = * * j jpq wC (31) According to Eq. (31) criteria involved in concordance set (C(p,q)) are represented by *j .   − − = +++ qjpjj qjpjj pq vv vv D (32) According to Eq. (32) criteria involved in discordance set (D(p,q)) are represented by +j 6-Relationships between alternatives are outranked by computing the averages of pqC and pqD that is represented by C and D respectively. According to this method alternative of pA outrank the alternative of qA if and only CCpq ≥ and DDpq ≤ conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. conditions are satisfied. By the way it should be control whether alternatives selected via this method comprise kernel. 7. Net concordance (Cp) and discordance (Dp) indexes, that are shown as be- low, are calculated. The ultimate ranking is obtained according to ordering Cp values from higher to lower and Dp values from lower to higher. 7-Net concordance ( pC ) and discordance ( pD ) indexes, that are shown as below, are calculated. The ultimate ranking is obtained according to ordering pC values from higher to lower and pD values from lower to higher.   = = −= m 1k m 1k kppkp CCC pk ≠ (33)   = = −= m 1k m 1k kppkp DDD pk ≠ (34) Results of research Purpose of this study is to assess the properties of different MCDM methods and compare the results of them in terms of evaluating the performance of 21 food firms listed in BIST by the help of financial ratios composing 5 year data set. For this purpose firstly financial ratios of each food firm listed in BIST are calculated. Eight financial ratios namely currency, acid test, cash, leverage, asset turnover, net profit/total assets, net profit/capital and net profit/net sales are considered. Then a survey evaluating the financial ratios was designed and applied for determining the weights of criteria and sub criteria. Survey was based on Saaty’s 9 point scale in order to weigh criteria and sub-criteria by pairwise comparisons in multilevel hierarchical structures. While defining the criteria and sub criteria, first of all, researchers made a depth literature review in order to develop the draft of the scale. 21 food companies listed in BIST are taken into the consideration as alternatives. Content validity is ensured by consulting to the experts’ opinion (especially academicians’ from finance field). After these procedures have been completed, data collection process started. Participants were selected from financial experts operated in universities, public and private sector. Participants were asked to compare four main criteria with respect to goal and all sub criteria within each main criteria on a pair-wise basis to determine their relative importance. As a result, 18 complete surveys were collected and analyzed. Weights of the criteria and sub criteria were acquired from the survey by using Buckley’s Column Geometric Mean approach, one of the fuzzy ranking methods. According to the results of Buckley’s Column Geometric Mean approach weights of ratios are given in Table 2. For all comparisons including criteria and sub criteria consistency ratios are under the 0.1 threshold level so comparisons made were consistent. (33) 7-Net concordance ( pC ) and discordance ( pD ) indexes, that are shown as below, are calculated. The ultimate ranking is obtained according to ordering pC values from higher to lower and pD values from lower to higher.   = = −= m 1k m 1k kppkp CCC pk ≠ (33)   = = −= m 1k m 1k kppkp DDD pk ≠ (34) Results of research Purpose of this study is to assess the properties of different MCDM methods and compare the results of them in terms of evaluating the performance of 21 food firms listed in BIST by the help of financial ratios composing 5 year data set. For this purpose firstly financial ratios of each food firm listed in BIST are calculated. Eight financial ratios namely currency, acid test, cash, leverage, asset turnover, net profit/total assets, net profit/capital and net profit/net sales are considered. Then a survey evaluating the financial ratios was designed and applied for determining the weights of criteria and sub criteria. Survey was based on Saaty’s 9 point scale in order to weigh criteria and sub-criteria by pairwise comparisons in multilevel hierarchical structures. While defining the criteria and sub criteria, first of all, researchers made a depth literature review in order to develop the draft of the scale. 21 food companies listed in BIST are taken into the consideration as alternatives. Content validity is ensured by consulting to the experts’ opinion (especially academicians’ from finance field). After these procedures have been completed, data collection process started. Participants were selected from financial experts operated in universities, public and private sector. Participants were asked to compare four main criteria with respect to goal and all sub criteria within each main criteria on a pair-wise basis to determine their relative importance. As a result, 18 complete surveys were collected and analyzed. Weights of the criteria and sub criteria were acquired from the survey by using Buckley’s Column Geometric Mean approach, one of the fuzzy ranking methods. According to the results of Buckley’s Column Geometric Mean approach weights of ratios are given in Table 2. For all comparisons including criteria and sub criteria consistency ratios are under the 0.1 threshold level so comparisons made were consistent. (34) Results of research Purpose of this study is to assess the properties of different MCDM methods and compare the results of them in terms of evaluating the performance of 21 food firms listed in BIST by the help of financial ratios composing 5 year data set. For this purpose firstly financial ratios of each food firm listed in BIST are cal- culated. Eight financial ratios namely currency, acid test, cash, leverage, asset turnover, net profit/total assets, net profit/capital and net profit/net sales are considered. Then a survey evaluating the financial ratios was designed and ap- plied for determining the weights of criteria and sub criteria. Survey was based ComParison of multi CritEria dECision making… 81 on Saaty’s 9 point scale in order to weigh criteria and sub-criteria by pairwise comparisons in multilevel hierarchical structures. While defining the criteria and sub criteria, first of all, researchers made a depth literature review in order to develop the draft of the scale. 21 food companies listed in BIST are taken into the consideration as alternatives. Content validity is ensured by consulting to the experts’ opinion (especially academicians’ from finance field). After these procedures have been complet- ed, data collection process started. Participants were selected from financial experts operated in universities, public and private sector. Participants were asked to compare four main criteria with respect to goal and all sub criteria within each main criteria on a pair-wise basis to determine their relative impor- tance. As a result, 18 complete surveys were collected and analyzed. Weights of the criteria and sub criteria were acquired from the survey by using Buckley’s Column Geometric Mean approach, one of the fuzzy ranking methods. According to the results of Buckley’s Column Geometric Mean approach weights of ratios are given in Table 2. For all comparisons including criteria and sub criteria consistency ratios are under the 0.1 threshold level so comparisons made were consistent. After the weights of criteria and sub criteria are deter- mined, criteria related values of 21 food firms listed in BIST within the period of 2011–2014 are obtained from firms’ websites. For ranking firms via TOPSIS, VIKOR and ELECTRE methodology EXCEL 2013 software is used. Table 2. Weights of ratios Ratios Weights Currency Ratio 0.215436 Acid Test Ratio 0.178542 Cash Ratio 0.077954 Leverage Ratio 0.270593 Asset Turnover Ratio 0.136721 Net Profit / Total Assets 0.059624 Net Profit / Capital 0.04073 Net Profit / Net Sales 0.020401 S o u r c e : own study. Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa82 According to the importance level of financial ratios leverage ratio was found as the most important criteria having the value of 0.270593. On the other hand ratio of net profit/net sales was obtained as the least important one hav- ing the value of 0.020401. values of each alternative and their rankings within the period of 2011–2014 are obtained via TOPSIS methodology and shown in Table 3. Table 3. RCi values and rankings of food firms according to descending order Firms 2011 2012 2013 2014 RCi Rank RCi Rank RCi Rank RCi Rank KERVT 0.50989 16 0.507408 18 0.379014 19 0.440693 18 OYLUM 0.534831 12 0.559625 7 0.452843 14 0.501208 14 ETILR 0.605787 4 0.610882 4 0.541313 2 0.5427 8 TACTR 0.537611 10 0.519595 15 0.447172 15 0.501864 13 TATGD 0.550522 7 0.545988 11 0.474083 9 0.565973 5 TKURU 0.491717 20 0.818974 1 0.70315 1 0.623132 3 TUKAS 0.502964 18 0.662827 2 0.416609 18 0.500321 15 ULKER 0.538916 9 0.621493 3 0.514934 4 0.729944 1 VANGD 0.54707 8 0.534708 12 0.493462 5 0.563026 6 YAPRK 0.61134 3 0.577484 5 0.493337 6 0.536027 9 DARDL 0.13309 21 0.164859 21 0.299255 20 0.23304 21 AVOD 0.576703 6 0.497203 19 0.470988 11 0.527845 10 PENGD 0.5056 17 0.525511 14 0.456942 12 0.506234 12 MRTGG 0.49905 19 0.568888 6 0.45329 13 0.394608 20 MANGO 0.53469 13 0.518172 16 0.42858 17 0.412764 19 MERKO 0.576858 5 0.558215 8 0.444587 16 0.55126 7 ALYAG 0.520311 15 0.546026 10 0.484433 7 0.521477 11 ARTOG 0.613169 2 0.466867 20 0.515367 3 0.595072 4 FRIGO 0.521809 14 0.516894 17 0.47542 8 0.488383 16 KRSAN 0.816341 1 0.525812 13 0.473192 10 0.465774 17 KENT 0.536358 11 0.555004 9 0.241906 21 0.623391 2 S o u r c e : own study. ComParison of multi CritEria dECision making… 83 According to the firms’ ranking related to RCi values KRSAN, ARTOG and YAPRK place top three position for 2011 respectively. On the contrary DARDL, TKURU and MRTGG place the last three position for 2011 respectively. While TKURU, TUKAS and ULKER perform as the top three food firms, DARDL, AR TOG and AVOD place the last three position for 2012. Top three food firms in the context of financial performance are ranked as TKURU, ETILR and ARTOG in 2013. This condition is valid for KENT, DARDL and KERVT as the last three food firms for 2013. Lastly while ULKER, KENT and TKURU perform as the top three food firms, DARDL, MRTGG and MANGO place the last three position for 2014. Some inconsistent outputs can be seen after applying the TOPSIS method. Firstly while TKURU places the 20th position in 2011 , it places the top three position in the range of 2012–2014. Similarly ARTOG places the top four posi- tion apart from the year of 2012. Other food firms suffered from the inconsist- ent results can be stated as KRSAN, TUKAS, MERKO and KENT respectively. By applying VIKOR methodology in order to obtain values of each alterna- tive consensus condition is considered and thus parameter (q) showing maxi- mum group benefit is used as 0.5. Ranking of food firms in ascending order af- ter acquiring values within the period of 2011–2014 are shown in Table 4. Table 4. Qa values (q=0.5) and rankings of food firms according to ascending order Firms 2011 2012 2013 2014 Qa Rank Qa Rank Qa Rank Qa Rank KERVT 0.531843 17 0.465892 14 0.71143 20 0.56407 17 OYLUM 0.522189 14 0.418068 10 0.607527 17 0.513941 16 ETILR 0.294855 2 0.220251 3 0.267991 2 0.353355 7 TACTR 0.489162 12 0.566464 20 0.671333 18 0.501523 15 TATGD 0.392574 6 0.417605 9 0.458707 7 0.293031 5 TKURU 0.629968 20 0 1 0 1 0.134067 2 TUKAS 0.613671 19 0.242336 4 0.547523 13 0.46239 12 ULKER 0.460664 8 0.192898 2 0.427773 5 0 1 VANGD 0.468493 10 0.51642 17 0.468869 9 0.29777 6 YAPRK 0.332044 4 0.400186 8 0.442589 6 0.424966 10 DARDL 1 21 1 21 1 21 1 21 AVOD 0.331932 3 0.529098 19 0.485923 11 0.415338 9 Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa84 Firms 2011 2012 2013 2014 Qa Rank Qa Rank Qa Rank Qa Rank PENGD 0.556397 18 0.491269 15 0.505888 12 0.456352 11 MRTGG 0.384604 5 0.396928 7 0.581811 15 0.656866 19 MANGO 0.464058 9 0.464351 13 0.582109 16 0.644862 18 MERKO 0.442859 7 0.463016 12 0.576545 14 0.359542 8 ALYAG 0.508062 13 0.429859 11 0.484551 10 0.480045 13 ARTOG 0.529193 15 0.31 5 0.339673 3 0.228217 4 FRIGO 0.5304 16 0.509877 16 0.419432 4 0.490496 14 KRSAN 0 1 0.519108 18 0.461385 8 0.664285 20 KENT 0.481138 11 0.382463 6 0.693706 19 0.192878 3 S o u r c e : own study. Acceptable advantage and acceptable stability conditions are satisfied for four years period (2011–2014). According to the acceptable advantage condi- tion difference between first and second alternative having Qa values are great- er than or equal the threshold value (DQ = 0.05 for k=21). However according to Qa values first alternative get the best score for values of both Sa and Ra, thus acceptable stability condition is satisfied. In terms of firms’ ranking related to Qa values KRSAN, ETILR and AVOD place the top three position for 2011 respectively. On the contrary DARDL, TK- URU and TUKAS place the last three position for 2011 respectively. While TK- URU, ULKER and ETILR perform as the top three food firms , DARDL, TACTR and AVOD place the last three position for 2012. Top three food firms in the context of financial performance are ranked as TKURU, ETILR and ARTOG in 2013. This condition is valid for DARDL , KERVT and KENT as the last three food firms for 2013. Lastly while ULKER, TKURU and KENT perform as the top three food firms, DARDL, KRSAN and MRTGG place the last three position for 2014. AVOD, TKURU, TUKAS, ARTOG, KRSAN and KENT are suffered from in- consistent results in the range of 2011–2014 after applying the VIKOR method. Cp values of each alternative and their rankings within the range of 2011–2014 are obtained via ELECTRE methodology and shown in Table 5. ComParison of multi CritEria dECision making… 85 Table 5. values and rankings of food firms according to descending order Firms 2011 2012 2013 2014 Rank Rank Rank Rank KERVT -5.05132 16 -3.74191 14 -9.79619 19 -8.49069 18 OYLUM 4.066299 6 2.892397 9 -6.53089 17 -3.76751 15 ETILR 9.312276 3 8.829443 3 12.0526 2 6.23837 6 TACTR 2.833143 10 -9.21342 20 -7.81541 18 -0.47822 12 TATGD 3.612507 8 -1.30122 12 4.990307 8 5.991833 7 TKURU -11.9987 20 11.41063 2 8.840116 3 5.630924 8 TUKAS -9.52866 18 0.739631 11 -5.77915 16 -2.30874 14 ULKER 3.275375 9 15.25167 1 6.124375 5 6.323224 5 VANGD 1.500985 11 -3.46261 13 5.315509 7 8.387681 3 YAPRK 9.50529 2 6.377541 4 8.801153 4 6.575883 4 DARDL -12.0556 21 -12.3511 21 -10.2635 20 -11.9765 19 AVOD 10.02192 1 -7.41517 18 0.272479 11 4.912043 9 PENGD -9.87913 19 -7.25223 17 -2.96534 12 -0.74082 13 MRTGG -1.17844 14 4.135935 7 -3.23204 13 -15.571 21 MANGO 4.783295 5 -5.55873 16 -11.3389 21 -15.2416 20 MERKO 4.983163 4 4.181412 6 -5.49547 15 3.600398 10 ALYAG -5.26583 17 2.052266 10 5.73018 6 1.877797 11 ARTOG -0.05753 13 4.457873 5 12.18496 1 8.963694 2 FRIGO -3.20064 15 -8.07618 19 1.343427 10 -4.0936 16 KRSAN 3.704686 7 -5.045 15 1.376178 9 -8.17546 17 KENT 0.616886 12 3.088766 8 -3.81432 14 12.34223 1 S o u r c e : own study. In terms of firms’ ranking related to Cp values AVOD, YAPRK and ETILR place the top three position for 2011 respectively. On the contrary DARDL, TK URU and PENGD place the last three position for 2011 respectively. While ULKER, TKURU and ETILR perform as the top three food firms, DARDL, TACTR and FRI- GO place the last three position for 2012. Top three food firms in the context of financial performance are ranked as ARTOG, ETILR and TKURU in 2013. This Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa86 condition is valid for MANGO, DARDL and KERVT as the last three food firms for 2013. Lastly while KENT, ARTOG and VANGD perform as the top three food firms, MRTGG, MANGO and DARDL place the last three position for 2014. AVOD, TKURU, MRTGG, ARTOG, KRSAN and KENT are suffered from inconsistent re- sults within the context of values. values of each alternative and their rank- ings within the range of 2011–2014 are obtained via ELECTRE methodology and shown in Table 6. Table 6. values and rankings of food firms according to ascending order Firms 2011 2012 2013 2014 Rank Rank Rank Rank KERVT 5.360736 15 3.98808 13 15.28188 21 11.06791 19 OYLUM 2.567986 13 1.38132 11 9.524144 18 5.549148 15 ETILR -12.0205 3 -8.84642 3 -16.2675 1 -6.17664 7 TACTR 3.148746 14 12.90877 21 10.95399 19 4.896926 13 TATGD -0.87463 12 0.46839 10 -3.09132 8 -5.6017 8 TKURU 17.76129 21 -15.8779 2 -15.5655 2 -9.97883 5 TUKAS 13.7527 20 -8.21683 4 8.663544 17 5.547872 14 ULKER -5.87499 7 -16.9419 1 -8.48023 5 -13.2718 1 VANGD -12.8804 2 5.598404 14 -4.95088 6 -12.71178 3 YAPRK -10.4432 4 -6.00319 7 -10.6987 4 -5.24372 9 DARDL 13.05345 19 8.289244 16 -4.05861 7 8.470648 17 AVOD -7.35979 6 6.77209 15 -1.01224 9 -3.01106 10 PENGD 13.0032 18 8.32757 17 6.5413 15 4.39811 12 MRTGG -2.4648 9 -5.44243 8 4.342252 14 17.82071 20 MANGO -4.91216 8 10.00535 19 15.138124 20 18.450842 21 MERKO -9.02815 5 -7.44385 6 7.129846 16 -8.13742 6 ALYAG -1.88785 10 2.200656 12 2.620903 12 -1.81698 11 ARTOG 9.226474 17 -7.88178 5 -11.91262 3 -12.18899 4 FRIGO 7.19831 16 9.184832 18 -0.426548 10 5.773014 16 KRSAN -16.0763 1 12.14587 20 0.744134 11 9.126434 18 KENT -1.25014 11 -4.61621 9 3.064286 13 -12.96266 2 S o u r c e : own study. ComParison of multi CritEria dECision making… 87 In terms of firms’ ranking related to Dp values KRSAN, VANGD and ETILR place the top three position for 2011 respectively. On the contrary TKURU, TU KAS and DARDL place the last three position for 2011 respectively. While ULKER, TKURU and ETILR perform as the top three food firms TACTR, KRSAN and MANGO place the last three position for 2012. Top three food firms in the context of financial performance are ranked as ETILR, TKURU and ARTOG in 2013. This condition is valid for KERVT, MANGO and TACTR as the last three food firms for 2013. Lastly while ULKER, KENT and VANGD perform as the top three food firms, MANGO, MRTGG and KERVT place the last three position for 2014. TUKAS, TKURU, MERKO, ARTOG, KRSAN, DARDL, VANGD and KENT are suffered from inconsistent results within the context of Dp values. According to the results of three methods while YAPRK and ETILR place the top five position, PENGD, TUKAS, TKURU and DARDL perform as the last five food firms in 2011. However, KRSAN perform the best financial perfor- mance and places the top position in 2011 with regard to RCi, Qa, and Dp values. That is true for AVOD in the context of Cp values. Apart from that while ARTOG places the top five position according to the values, it places the last five one considering Dp values. TKURU, ULKER and ETILR place in the top five position for all ranking methods in 2012. But all ranking methods are not agree with firms placing in the last five position for 2012. While TKURU, ULKER, ARTOG and ETILR perform as the top five food firms in 2013, this condition is valid for KERVT placing as the last five food firms according to all ranking methods with regard to RCi, Qa, Cp and Dp values. Lastly common firms placing in the top five position for all ranking methods are stated as ULKER, KENT and ARTOG in 2014. MRTGG, MANGO, KERVT, DARDL and KRSAN are common firms placing in the last five position with respect to RCi, Qa, Cp and Dp values in 2014. Recommendations and future research In this study performances of twenty one food firms listed in BIST are ana- lyzed in the context of different financial ratios and ranked via different MCDM methods namely TOPSIS, VIKOR and ELECTRE within the period of 2011–2014. For this purpose weights of financial ratios are obtained by using Buckley’s Column Geometric Mean approach, one of the fuzzy ranking methods. There is not enough study based on comparing the performances of food firms listed in BIST via fuzzy ranking integrated MCDM methods. Ultimately all of MCDM Namık Kemal Erdoğan, Serpil Altınırmak, Çağlar Karamaşa88 methods which are based on weighted financial ratios give the similar ranking results by years. 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