The concept of inverse semihypergroup is a generalization of the concept of inverse semigroup. In this paper we defined an orthodox semihypergroup S as it is a regular semihypergroup in which the set ...of idempotents of S forms a subsemihypergroup. We also presented a new definition of inverse semihypergroup S as each element x ∈ S has a unique inverse s −1 in S, and we provided many results related to inverse semihypergroups, regular semihypergroups and orthodox semihypergroups
In this paper, we define and study the concept of the factorizable semihypergroup, i.e., a semihypergroup that can be written as a hyperproduct of two proper sub-semihypergroups. We consider some ...classes of semihypergroups such as regular semihypergroups, hypergroups, regular hypergroups, and polygroups and investigate their factorization property.
This paper deals with a particular class of hyperstructures called semihypergroups, which is a generalization of semigroups. We introduce the notions of SU-qausi hyperideal, SU-bi-hyperideal, ...SU-generalized bi-hyperideal, SU-interior hyperideal and discuss several properties of these hyperideals. We also characterize regular and intra-regular semihypergroups by the properties of their SU-hyperideals.
We first introduce the notion of some interval-valued fuzzy hyperideals of a semihypergroup and present some important structural results. Then we find some inter-relations between interval-valued ...fuzzy hyperideals and obtain some characterizations of regular semihypergroups, intra-regular semihypergroups by using interval-valued fuzzy hyperideals of semihypergroups.
In this paper, we introduce prime, strongly prime, semiprime, irreducible and strongly irreducible soft bi-hyperideals of a semihypergroup over an initial universe U. We characterize regular and ...intra-regular semihypergroups in terms of these soft bi-hyperideals.
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