Approximate fuzzy preorders and equivalences

Authors:
Dionís Boixader;J. Recasens
Affiliations:
E.T.S. d'Arquitectura del Vallès, Universitat Politècnica de Catalunya, Sant Cugat del Vallès, Spain;E.T.S. d'Arquitectura del Vallès, Universitat Politècnica de Catalunya, Sant Cugat del Vallès, Spain
Venue:
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Year:
2009

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Abstract

Although Fuzzy Preorders and Fuzzy Equivalences are well established types of fuzzy relations, they are defined in terms of properties to be fulfilled in a crisp way. In this paper we relax those requirements by making them gradual in some way. As a result, a number of relations which are not strictly reflexive, symmetric or transitive with respect to any t-norm T, would be regarded as (Approximate) Fuzzy Preorders or Equivalences.