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On the construction of fuzzy preference structures
Author(s) -
Bufardi Ahmed
Publication year - 1998
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/(sici)1099-1360(199805)7:3<169::aid-mcda189>3.0.co;2-3
Subject(s) - transitive relation , mathematics , preference relation , fuzzy logic , preference , binary relation , generalization , binary number , norm (philosophy) , relation (database) , algebra over a field , pure mathematics , discrete mathematics , computer science , artificial intelligence , combinatorics , arithmetic , data mining , mathematical analysis , statistics , epistemology , philosophy
In this paper, we analyse the generalization of the classical method of the construction of a preference structure from a reflexive binary relation to the case of fuzzy binary relations. According to our approach, there are two interesting fuzzy preference structures we can construct from a given reflexive fuzzy binary relation. These two fuzzy preference structures correspond to the two extreme solutions of the system of functional equations in the method of Fodor and Roubens. We also prove that only one of two fuzzy preference structures allows its fuzzy relation of strict preference to be transitive with respect to the φ ‐transform of the Lukasiewicz t‐norm when the reflexive fuzzy relation it is constructed from is also transitive with respect to the same t‐norm. © 1998 John Wiley & Sons, Ltd.