FUZZY HYPER KS-SEMIGROUPS - Davvaz, Bijan; Vicedo, Ann Leslie O.; Vilela, Jocelyn P. (Italian Journal of Pure and Applied Mathematics, 2015)
Hyperstructure theory is applied to KS-semigroups, an algebra related to BCK-algebra and semigroup and thus, the notion of hyper KS-semigroups is introduced. In this paper, the concept of fuzzy sets is applied to hyper KS-semigroups. In this fuzzification, the notions of fuzzy hyper subKS-semigroups and fuzzy hyper KS-ideals are introduced and relationships among them are investigated. Using the concept of upper level subsets, relationships between hyper subKS-semigroups (resp. hyper KS-ideals) and fuzzy hyper subKS-semigroups (resp. fuzzy hyper KS-ideals) are established. Finally, under a homomorphism f : G \(\longrightarrow\) H of hyper KS-semigroups, it is shown that the pre-image of a fuzzy hyper KS-ideal of H is a fuzzy hyper KS-ideal of G.