# Weak Fuzzy Equivalence and Equality Relations

• Branimir Šešelja
• Andreja Tepavčević
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5909)

## Abstract

Weak fuzzy (lattice valued) equivalences and equalities are introduced by weakening the reflexivity property. Every weak fuzzy equivalence relation on a set determines a fuzzy set on the same domain. In addition, its cut relations are crisp equivalences on the corresponding cut subsets. Analogue properties of weak fuzzy equalities are presented. As an application, fuzzy weak congruence relations and fuzzy identities on algebraic structures are investigated.

## Keywords and phrases

lattice-valued fuzzy set lattice-valued fuzzy relation block cut fuzzy equivalence fuzzy equality fuzzy identity

## AMS Mathematics Subject Classification (2000)

primary 03B52 03E72 secondary 06A15

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