The purpose of this paper is the study of non-weak commutative hypergroups associated with hypergraphs. In this regards, we construct a hyperoperation on the set of vertices of hypergraph and obtain some results and characterizations of them. Moreover, according to this hyperoperation, we investigate conditions under which the Hypergroupoid is a join space hypergroup. Finally, we present an application to marketing social network.

In this paper, we present some primary methods to define a Hypergroupoid by algorithm. Then, we present algorithms for checking if it is closed under ο, associativity, weak associativity, commutativity, weak commutativity, establishing the reproduction axiom, determining the type of a Hypergroupoid  (H,ο) and the type of a morphism f in a Hypergroupoid (H,ο). The goal of this paper is to provide algorithms for checking the basic features and morphisms in algebraic hyperstructures. Our attention is on algorithms for algebraic hyperstructures with one hyperoperation (i.e. Hypergroupoids). The algorithms can be developed for other algebraic hyperstructures.

The aim of this paper is the study of the sequence of join spaces and fuzzy subsets associated with a Hypergroupoid. In this paper we give some properties of the membership function m~Äcorresponding to the direct product of two Hypergroupoids and we determine the fuzzy grade of the Hypergroupoid (H x H, Ä) in a particular case.

In this note, we introduce the concept of topologically simple semihypergroup and determine when topological simplicity of a complete subsemihypergroup of a semihypergroup implies its simplicity from algebraic point of view.

In this paper, we generalize the definition of the relation $\beta$ for Hypergroupoids. Also, we presents new theorems for calculating the members of the relation $\beta$ and by using new theorems, we provide algorithms to calculate the members of the relation $\beta$. Finally, as an additional section, implementing the algorithms in Maple is presented, as well as some examples.

On a Hypergroupoid one can define a topology such that the hyperoperation is pseudocontinuous or continuous. In this paper we extend these concepts to the fuzzy case. We give a connection between the classical and the fuzzy (pseudo)continuous hyperoperations.

The purpose of this paper is the study of Cayley graph associated to a semihy-pergroup(or hypergroup). In this regards , rst we associate a Cayley graph to every semi-hypergroup and then we study the properties 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 the properties of a Cayley graph associated to a semihypergroup is completely di, erent with respect to the Cayley graph associated to a semigroup(group). Also, we brie y discuss on category of Cayley graphs associated to semi-hypergroups and construct a functor from this category to the category of digraphs. Finally, we give an application the Cayley graph of a Hypergroupoid to a social network.