A note on group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment

In a very recent paper by Kuo et al. [M.S. Kuo, G.H. Tzeng, W.C. Huang, Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment, Mathematical and Computer Modelling 45 (3-4) (2007) 324-339], a fuzzy multicriteria decision analysis method based on the concepts of ideal and anti-ideal points was presented. This note illustrates with a numerical example that the method presented by Kuo et al. is not correct and can evaluate more than one decision alternative as the best even if they are not Pareto optimal at all. The fundamental reason for this is because the closeness coefficient values adopted by the authors do not reflect the superiority or inferiority of decision alternatives and cannot be used for ranking purpose. Corrections to their method are therefore suggested.

[1]  Chung-Hsing Yeh,et al.  A practical approach to fuzzy utilities comparison in fuzzy multicriteria analysis , 2004, Int. J. Approx. Reason..

[2]  Yufei Yuan.  Criteria for evaluating fuzzy ranking methods , 1991 .

[3]  J. Buckley.  Ranking alternatives using fuzzy numbers , 1985 .

[4]  Gin-Shuh Liang,et al.  Using fuzzy MCDM to select partners of strategic alliances for liner shipping , 2005, Inf. Sci..

[5]  G. Bortolan,et al.  A review of some methods for ranking fuzzy subsets , 1985 .

[6]  Chen-Tung Chen,et al.  A fuzzy approach for supplier evaluation and selection in supply chain management , 2006 .

[7]  Shinhong Kim,et al.  An integrated approach for interdependent information system project selection , 2001 .

[8]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[9]  Tien-Chin Wang,et al.  Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment , 2007, Expert Syst. Appl..

[10]  Gülçin Büyüközkan,et al.  A two phase multi-attribute decision-making approach for new product introduction , 2007, Inf. Sci..

[11]  Chung-Hsing Yeh,et al.  Fuzzy multicriteria analysis for performance evaluation of bus companies , 2000, Eur. J. Oper. Res..

[12]  Juan Manuel Campos Benítez,et al.  Using fuzzy number for measuring quality of service in the hotel industry , 2007 .

[13]  Juite Wang,et al.  A fuzzy multicriteria group decision making approach to select configuration items for software development , 2003, Fuzzy Sets Syst..

[14]  T. Chu.  Selecting Plant Location via a Fuzzy TOPSIS Approach , 2002 .

[15]  K. Nakamura.  Preference relations on a set of fuzzy utilities as a basis for decision making , 1986 .

[16]  Rong Li.  Fuzzy method in group decision making , 1999 .

[17]  Soung Hie Kim,et al.  Using analytic network process and goal programming for interdependent information system project selection , 2000, Comput. Oper. Res..

[18]  Evangelos Triantaphyllou,et al.  Development and evaluation of five fuzzy multiattribute decision-making methods , 1996, Int. J. Approx. Reason..

[19]  J. Buckley,et al.  Fuzzy hierarchical analysis , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[20]  Ta-Chung Chu,et al.  Facility Location Selection Using Fuzzy TOPSIS Under Group Decisions , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[21]  C. Carlsson.  Tackling an MCDM-problem with the help of some results from fuzzy set theory , 1982 .

[22]  Chen-Tung Chen,et al.  Aggregation of fuzzy opinions under group decision making , 1996, Fuzzy Sets Syst..

[23]  Love Ekenberg,et al.  A framework for analysing decisions under risk , 1998 .

[24]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[25]  Taho Yang,et al.  Multiple-attribute decision making methods for plant layout design problem , 2007 .

[26]  G. Tzeng,et al.  Evaluating sustainable fishing development strategies using fuzzy MCDM approach , 2005 .

[27]  S. Zahariev,et al.  An approach to group choice with fuzzy preference relations , 1987 .

[28]  Chiang Kao,et al.  Fractional programming approach to fuzzy weighted average , 2001, Fuzzy Sets Syst..

[29]  Gin-Shuh Liang,et al.  Fuzzy MCDM based on ideal and anti-ideal concepts , 1999, Eur. J. Oper. Res..

[30]  Hepu Deng,et al.  Multicriteria analysis with fuzzy pairwise comparison , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[31]  T. Chu,et al.  A Fuzzy TOPSIS Method for Robot Selection , 2003 .

[32]  Taho Yang,et al.  Multiple attribute decision-making methods for the dynamic operator allocation problem , 2007, Math. Comput. Simul..

[33]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[34]  Ying-Ming Wang,et al.  Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment , 2006, Expert Syst. Appl..

[35]  Mohammad Izadikhah,et al.  Extension of the TOPSIS method for decision-making problems with fuzzy data , 2006, Appl. Math. Comput..

[36]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[37]  Chung-Hsing Yeh,et al.  Multi-criteria analysis for dredger dispatching under uncertainty , 1999, J. Oper. Res. Soc..

[38]  Navee Chiadamrong,et al.  An integrated fuzzy multi-criteria decision making method for manufacturing strategies , 1999 .

[39]  E. Lee,et al.  Comparison of fuzzy numbers based on the probability measure of fuzzy events , 1988 .

[40]  Ali Shanian,et al.  TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell , 2006 .

[41]  Sheng-Hshiung Tsaur,et al.  The evaluation of airline service quality by fuzzy MCDM. , 2002 .

[42]  Mao-Jiun J. Wang,et al.  A MULTIPLE CRITERIA LINGUISTIC DECISION-MODEL (MCLDM) FOR HUMAN DECISION-MAKING , 1994 .

[43]  Gwo-Hshiung Tzeng,et al.  Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment , 2007, Math. Comput. Model..

[44]  E. Stanley Lee,et al.  Fuzzy weighted average: The linear programming approach via Charnes and Cooper's rule , 2001, Fuzzy Sets Syst..

[45]  Gwo-Hshiung Tzeng,et al.  Combining grey relation and TOPSIS concepts for selecting an expatriate host country , 2004, Math. Comput. Model..

[46]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[47]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.