Preprint Article Version 1 This version is not peer-reviewed

Decomposition and Intersection of Two Fuzzy Numbers for the Fuzzy Preference Relations

Version 1 : Received: 11 September 2017 / Approved: 11 September 2017 / Online: 11 September 2017 (16:44:07 CEST)

A peer-reviewed article of this Preprint also exists.

Tang, H.-C. Decomposition and Intersection of Two Fuzzy Numbers for Fuzzy Preference Relations. Symmetry 2017, 9, 228. Tang, H.-C. Decomposition and Intersection of Two Fuzzy Numbers for Fuzzy Preference Relations. Symmetry 2017, 9, 228.

Journal reference: Symmetry 2017, 9, 228
DOI: 10.3390/sym9100228

Abstract

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. Among which, the fuzzy preference relation is the reasonable one to represent preference relation by a fuzzy membership function. This paper studies the Nakamura’s and Kołodziejczyk’s preference relations. Eight cases of representing different level of overlapping between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of decomposition and intersection of two fuzzy numbers for the Nakamura’s and Kołodziejczyk’s preference relations of these test cases. The results indicate that the decomposition and intersection can affect the fuzzy preference relations, thereby the final total order relation of fuzzy numbers.

Subject Areas

fuzzy number; ranking; preference relation

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