Fuzzy Decision-Making Based on Likelihood-Based Comparison Relations

In this paper, we present a new fuzzy decision-making method, which is based on likelihood-based comparison relations. First, we introduce the concepts of likelihood-based comparison relations for intervals. Then, we propose the concept of likelihood-based comparison relations for type-1 fuzzy sets and interval type-2 fuzzy sets. Then, we present a new method to rank fuzzy sets by using fuzzy targets based on the proposed likelihood-based comparison relations for fuzzy sets. Finally, we present a new fuzzy decision-making method based on the proposed likelihood-based comparison relations for fuzzy sets and the proposed fuzzy ranking method. The proposed fuzzy decision-making method has the advantage that the evaluated values can either be represented by crisp values, intervals, type-1 fuzzy sets or interval type-2 fuzzy sets. It can overcome the drawbacks of Huynh et al.'s method due to the fact that Huynh et al.'s method cannot deal with the ranking of interval type-2 fuzzy sets for fuzzy decision-making and cannot distinguish the ranking order between the alternatives in some situations.

[1]  Wolfgang Hauke.  Fuzzy Multiple Attribute Decision Making (Fuzzy-MADM) , 1998 .

[2]  M. Vila,et al.  A procedure for ranking fuzzy numbers using fuzzy relations , 1988 .

[3]  Ronald R. Yager,et al.  Fuzzy modeling for intelligent decision making under uncertainty , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Jerry M. Mendel,et al.  A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets , 2009, Inf. Sci..

[5]  Ramesh Jain,et al.  DECISION MAKING IN THE PRESENCE OF FUZZY VARIABLES , 1976 .

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

[7]  Ronald R. Yager,et al.  A context-dependent method for ordering fuzzy numbers using probabilities , 2001, Inf. Sci..

[8]  Shyi-Ming Chen,et al.  A new method for fuzzy decision-making based on likelihood-based comparison relations , 2009, 2009 International Conference on Machine Learning and Cybernetics.

[9]  Ivan Popchev,et al.  Comparison of clusters from fuzzy numbers , 1998, Fuzzy Sets Syst..

[10]  Waldemar Koodziejczyk.  Orlovsky's concept of decision-making with fuzzy preference relation—Further results , 1986 .

[11]  Cerry M. Klein,et al.  New algorithm for the ranking procedure in fuzzy decision-making , 1989, IEEE Trans. Syst. Man Cybern..

[12]  Ronald R. Yager,et al.  Decision making with fuzzy probability assessments , 1999, IEEE Trans. Fuzzy Syst..

[13]  Ronald R. Yager,et al.  Including decision attitude in probabilistic decision making , 1999, Int. J. Approx. Reason..

[14]  H. B. Mitchell.  Pattern recognition using type-II fuzzy sets , 2005, Inf. Sci..

[15]  Jee-Hyong Lee,et al.  A method for ranking fuzzy numbers and its application to decision-making , 1999, IEEE Trans. Fuzzy Syst..

[16]  J. Baldwin,et al.  Comparison of fuzzy sets on the same decision space , 1979 .

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

[18]  Van-Nam Huynh,et al.  A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making , 2008, IEEE Transactions on Fuzzy Systems.

[19]  Van-Nam Huynh,et al.  A satisfactory-oriented approach to multiexpert decision-making with linguistic assessments , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Piero P. Bonissone,et al.  A Linguistic Approach to Decisionmaking with Fuzzy Sets , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[22]  J. J. Saade,et al.  Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty , 1992 .

[23]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[24]  H. B. Mitchell.  Ranking type-2 fuzzy numbers , 2006, IEEE Transactions on Fuzzy Systems.

[25]  Ramesh C. Jain.  A procedure for multiple-aspect decision making using fuzzy sets , 1977 .

[26]  K. Kim,et al.  Ranking fuzzy numbers with index of optimism , 1990 .

[27]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[28]  H. Lee-Kwang,et al.  Ranking fuzzy values with satisfaction function , 1994 .

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