OR Fuzzy Operations Research Preference Relations On A Set Of Fuzzy Utilities As A Basis For Decision Making.
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Preference Relations On A Set Of Fuzzy Utilities As A Basis For Decision Making. Kazuo NAKAMURA Industrial Products Research Institute, 1-1-4, Yatabe-machi, Higashi, Tsukuba-gun, Ibaraki 305, Japan Received January 1985 Revised May 1985 In fuzzy decision problems, we often encounter situations of choosing among alternatives which are assigned fuzzy utilities. These problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities. In the literature, however, there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory. This paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities. Then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making. This procedure employs the concepts of the extended minimum and the Hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities. Finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making. Keywords: Preference, Utility, Reasonable ordering, Decision making, Fuzzy relation, Reciprocal relation, Transitivity, Comparability, Weak ordering, Greatest upper set, Greatest lower set.
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