Weak Fuzzy Equivalence and Equality Relations
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.