In this paper, we introduce the concept of a locally associative LA-semihypergroup by generalizing the idea of a locally associative LA-semigroup given in Mushtaq–Yusuf, 1979, and study an (m,n)regular class of a locally associative LA-semihypergroup. We give some examples to connect an LA-semihypergroup with commutative hypergroups and commutative semihypergroups. We also characterize a locall...

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...

we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

The notion of bipolar fuzzy set was initiated by Lee (2000) as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study on bipolar ( ,   )-fuzzy sets in -semihypergroups. By using the concept of bipolar ( ,   )-fuzzy sets (Yaqoob and Ansari, 2013), we introduce the ...

In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

An h-relation on a non-empty set S is in fact a relation from S to the power set P (S) of S. Here, in this paper, it is shown that the semigroup of binary relations on a set S can be embedded as a subsemigroup into the semigroup of h-relations on S(with restpect to a suitably defined operation). We have introduced and studied here two types of reflexivities, symmetries and transitivities of h-r...

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...

In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.

We consider the fundamental relation on a semihypergroup to interpret the lower and upper approximations as subsets of the fundamental semigroup / and we give some results in this connection. Also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary...