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


Peker S., Shikhlinskaya R., Nasibov E.

APPLIED AND COMPUTATIONAL MATHEMATICS, vol.19, no.1, pp.34-46, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2020
  • Journal Name: APPLIED AND COMPUTATIONAL MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.34-46
  • Keywords: Decision Making, Fuzzy Number, Fuzzy Relation, Ranking, RECIPROCAL RELATIONS, TRANSITIVITY
  • Dokuz Eylül University Affiliated: Yes

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 alpha-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.