On the representations of L-equivalence relations on L-fuzzy sets with applications to locally vague environments

DEMİRCİ M.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.49, no.3, pp.334-354, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1080/03081079.2020.1730359
  • Journal Name: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Sociological abstracts, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.334-354
  • Keywords: Fuzzy set, fuzzy equality, fuzzy similarity, fuzzy equivalence, vague environment, fuzzy point, EQUALITY RELATIONS, FOUNDATIONS
  • Akdeniz University Affiliated: Yes

Abstract

L-equivalence relations on L-fuzzy sets, equivalent to L-valued equalities on ordinary sets, are modelling fuzzy similarity of two objects that are partial members of a fuzzily defined set. This paper deals with construction and representation properties of L-equivalence relations on L-fuzzy sets. To this end, we set up a method for constructing them by means of quasi-pseudo-metrics, and then point out how L-equivalence relations on L-fuzzy sets are represented by families of L-fuzzy subsets of L-fuzzy sets. The present results are applied to locally vague environments to elucidate conceptual structures of locally vague environments, and to show how the points in a locally vague environment are described.