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Decomposition and Intersection of Two Fuzzy Numbers for Fuzzy Preference Relations

Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, Kaohsiung 80778, Taiwan
Symmetry 2017, 9(10), 228;
Received: 11 September 2017 / Revised: 7 October 2017 / Accepted: 9 October 2017 / Published: 14 October 2017
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
PDF [1588 KB, uploaded 17 October 2017]


In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. The fuzzy preference relation is the reasonable representation of preference relations by a fuzzy membership function. This paper studies Nakamura’s and Kołodziejczyk’s preference relations. Eight cases, each representing different levels of overlap between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of the decomposition and intersection of two fuzzy numbers through eight extensive test cases. The results indicate that decomposition and intersection can affect the fuzzy preference relations, and thereby the final ranking of fuzzy numbers. View Full-Text
Keywords: fuzzy number; ranking; preference relations fuzzy number; ranking; preference relations

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

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