Strict fuzzy orderings with a given context of similarity


Bodenhofer U., DEMİRCİ M.

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol.16, no.2, pp.147-178, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1142/s021848850800511x
  • Journal Name: INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.147-178
  • Keywords: fuzzy equivalence relations, fuzzy orderings, fuzzy relations, partial fuzzy orderings, strict fuzzy orderings, VALUED EQUIVALENCE-RELATIONS, PREFERENCE STRUCTURES, LUKASIEWICZ TRIPLETS, BINARY RELATIONS, T-NORMS, SETS, DEFINITION, PARTITIONS, LATTICES, AXIOMS
  • Akdeniz University Affiliated: Yes

Abstract

This paper introduces strict fuzzy orderings in the framework of similarity-based fuzzy orderings, i.e. where a context of similarity/indistinguishability is given by means of a fuzzy equivalence relation. We consider how to construct strict fuzzy orderings from partial fuzzy orderings and vice versa. The appropriateness of the concepts introduced in this paper is underlined by theoretical results and examples. We observe that the strongest results are achieved if the underlying triangular norm induces an involutive residual negation.