Fuzzy Credibility Relation Method for Multiple Criteria Decision-Making Problems

Combining the concepts of fuzzy set theory, entropy, ideal, and grey relation analysis, a fuzzy grey relation method for multiple criteria decision-making problems is proposed. First, triangular fuzzy numbers and linguistic values characterized by triangular fuzzy numbers are used to evaluate the importance weights of all criteria and the superiority of all alternatives versus various criteria above the alternative level. Then, the concept of entropy is utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Furthermore, using the concepts of ideal, the grey ration grades of various alternatives versus ideal solution are ranked to determine the best alternative. Finally, a numerical example of selecting most appropriate company to build a new highway is used to demonstrate the applicability of proposed method. The study results show that this method is an effective means for tackling MCDM problems in fuzzy and grey environments.

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

[2]  Ching-Lai Hwang,et al.  Methods for Multiple Attribute Decision Making , 1981 .

[3]  Jean-Marc Martel,et al.  A fuzzy outranking relation in multicriteria decision making , 1986 .

[4]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[5]  Ralph E. Steuer,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years , 1992 .

[6]  Bernard Roy,et al.  Problems and methods with multiple objective functions , 1971, Math. Program..

[7]  Jaap Spronk,et al.  Multiple Criteria Decision Methods and Applications , 1985 .

[8]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[9]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[10]  Jacques Teghem,et al.  An interactive decision support system (IDSS) for multicriteria decision aid , 1989 .

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

[12]  Bertrand Mareschal,et al.  Prométhée: a new family of outranking methods in multicriteria analysis , 1984 .

[13]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[14]  A. Pascu.  Operational research '81: J.P. Brans (Ed.) Proceedings of the Ninth IFORS International Conference on Operational Research, Hamburg, Germany, July 20–24, 1981, North-Holland, Amsterdam, 1981, xx + 984 pages, Dfl.250.000 , 1982 .

[15]  D. E. Bell,et al.  Conflicting Objectives in Decisions , 1978 .

[16]  Y. Ku,et al.  Introduction to fuzzy arithmetic—theory and applications : Arnold Kaufmann and Madan M. Gupta. 351 pages, diagrams, figures. Van Nostrand Reinhold Company, New York, 1985. , 1986 .

[17]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[18]  Rudolf Vetschera.  An interactive outranking system for multiattribute decision making , 1988, Comput. Oper. Res..

[19]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

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

[21]  Gerhard O. Mensch,et al.  TIMS Studies in the management sciences : Burton V. Dean and Joel L. Goldhar (eds.), Management of Research and Innovation, North-Holland Publishing Company, Amsterdam, Vol. 15, 1980, 300 pp. , 1983 .

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

[23]  S. S. Alam,et al.  Partial preference structure with fuzzy relations for MCDM problems , 1989 .

[24]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

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

[26]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..