Fuzzy relations and fuzzy functions

On fuzzy congruences of a type-B semigroup I

“…In 1971, Rosenfeld [18] explained the notion of a fuzzy subgroup of a group with the notion of fuzzy subsets of a set. The development of fuzzy abstract algebra has since been greatly inspired by the results of the research [2,8,14,15,19,20,21,22]. Following the formulation of fuzzy groups by Rosenfeld, many researchers have been engaged in extending the concepts and results of pure algebra to the broader framework of the fuzzy setting, although not all results in algebra can be fuzzified.…”

“…Following the formulation of fuzzy groups by Rosenfeld, many researchers have been engaged in extending the concepts and results of pure algebra to the broader framework of the fuzzy setting, although not all results in algebra can be fuzzified. As we know, the concepts of fuzzy equivalent relations on a set were introduced by Murali [14] and Nemitz [15], respectively. Samhan [19] defined fuzzy congruence relations on semigroups.…”

Fuzzy Mappings and Fuzzy Equivalence Relations

“…Subsequently, Goguen [2], Murali [3] and Ovchinnikov [5], etc., have studied fuzzy relations in various contents. Furthermore, Nemitz [4] have investigated fuzzy relations connected with equivalence relations and fuzzy functions. In particular, more recently, Demirci [1] studied fuzzy equalities and fuzzy mappings.…”

Fuzzzy Functions and Fuzzy Partially Ordered Sets

“…Thus the concept of Cartesian product plays an important role in the usual theory of relations and functions. Almost all authors have worked with fuzzy relations without referring to what may be called fuzzy Cartesian product (See [1,3,7,8]). …”