Fuzzy hypersemigroups

Abstract

We introduce the notions of fuzzy hypersemigroup, fuzzy hypergroup, fuzzy hyperideal, homomorphism, hyper congruence, fuzzy homomorphism, fuzzy hypercongruence. The purpose of this note is the study of some characterization of fuzzy hypersemigroup, fuzzy hyperideal of a fuzzy hypersemigroup and homomorphism and hypercongruence on a hypersemigroup.

Fuzzy hypermodules

“…The fuzzy semihypergroup notion was introduced and studied in [11]. In this paper, a little change is done, which consists in using F * (S), instead of F (S), as in [11].…”

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

“…The relationships between the fuzzy sets and algebraic hyperstructures have been considered by Corsini, Davvaz, Kehagias, Leoreanu, Vougiouklis, Yin, Zhan and others. The reader is refereed to [5,22,26,28,40,43,48,50,51]. Also, the relationships between the fuzzy sets and n-ary algebraic hyperstructures have been considered by Corsini et al in [10-12, 20, 29, 46].…”

Isomorphism theorems of fuzzy hypermodules

“…Finally, the third group of papers on fuzzy hyperstructures associates a fuzzy set with each pair of elements of a set. This idea was introduced by Corsini and Tofan in [9] and then, Sen, Ameri and Chowdhury introduced and analyzed fuzzy semihypergroups in [26]. This idea was extended to fuzzy hyperrings and fuzzy hypermodules by Davvaz and Leoreanu-Fotea in [20] and [21].…”