In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hype...

We study closure properties with respect to products for hypergroupoids, semihypergroups and hypergroups associated to binary relations. Using some basic category theory tools, from a certain point, the investigation turns into studying closure properties with respect to direct products for some classes of monounary multialgebras.

The main purpose of this paper is to introduce the concept of (Γ, n)semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category (Γ, n)-semihypergrous and the category semigroups. Moreover, we introduce and study complete part. Finally, we obtain some new results and some fundamental theorems in this respect.

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them. 2010 AMS Classification: 03B60, 20A05, 20N20, 97H40

the aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $s_{h}$ and  $t_{h},$ respectively. it is shown that $t_{h}=s_{h}$ if and only if $beta=beta^{*}.$ we also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

In this article we generalize the notion of complete parts, by introducing a weaker condition in definition. Using this generalization we define and analyse a new class of semihypergroups, which are called weak complete semihypergroups. Complete parts were introduced about 40 years ago by M. Koskas and they represent a basic notion of hyperstucture theory, utilized in constructing an important ...

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups...

Generalizing the concepts of (∈,∈ ∨q)-fuzzy hyperideal, (∈,∈ ∨q)-fuzzy quasi-hyperideal and (∈,∈ ∨q)-fuzzy bihyperideal, the notions of (∈,∈ ∨qk)-fuzzy hyperideal, (∈,∈ ∨qk)-fuzzy quasi-hyperideal and (∈,∈ ∨qk)-fuzzy bi-hyperideal are defined. Using these notions, different classes of semihypergroups are characterized.