COMPARISON OF FUZZY NUMBERS USING LEFT/RIGHT SIDES OF LEVEL SETS

Abstract

Comparison is the most important operation in Decision Making (DM) problems. In case of crisp numbers there is not a problem but comparison of Fuzzy Numbers (FN) involves many problems. This study handles a level set approach to compare fuzzy numbers. The level sets are compared in accordance with ”all”-”all” ”all” ”some” ”some” ”all” and ”some” ”some” quantifiers. This case reflects the optimistic/pessimistic approaches of a decision maker. This four approaches handle the left/left left/right right/left right/right sides of α-cuts level of two fuzzy numbers. The proposed relations are investigated in accordance with the ranking of fuzzy numbers and all relations are analyzed whether they satisfy or not the reflexive transitive symmetric antisymmetric partial ordering properties of relations. In addition basic rules for the comparison of two fuzzy numbers are given. © 2023 Elsevier B.V. All rights reserved.