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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.
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.
Keywords
fuzzy number; ranking; preference relation
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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