In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups (resp. neutro-hypergroups). We investigate the property of anti-semihypergroups (resp. anti-hypergroups). We also give a new alternative of neutro-hyperoperations (resp. anti-hyperoperations), neutro-hyperoperation-sophications (resp. anti-hypersophications). Moreover, we show that these new concepts are different from classical concepts by several examples.

In this paper, we present some connections between graph theory and hyperstructure theory. In this regard, we construct a hypergroupoid by defining a hyperoperation on the set of degrees of vertices of a hypergraph and we call it a degree hypergroupoid. We will see that the constructed hypergroupoid is always anHv-group. We will investigate some conditions on a degree hypergroupoid to have a hypergroup. Further, we study the degree hypergroupoid associated with Cartesian product of hypergraphs. Finally, the fundamental relation and complete parts of a degree hypergroupoid are studied.

The purpose of this paper is the study of hypergroups associated with hypergraphs. In this regard, we construct a hypergroupoid by defining a hyperoperation on the set of degrees of vertices of a hypergraph. We will see that the constructed hypergroupoid is always an Hv-group. We will investigate some conditions to have a hypergroup.

Let G be an abelian group with identity e. Let R be a graded multiplicative hyperring and δ : Igr(R) → Igr(R) be an expansion function of Igr(R), where Igr(R) is the set of all graded hyperideals of R. In this paper, we introduce and study the concepts of graded δ-primary hyperideals of R and graded 2-absorbing δ-primary hyperideals of R which are the extended classes of graded prime and graded 2- absorbing hyperideals of R, respectively. Moreover, we give the basic properties of these new types of graded hyperideals and investigate the relations among these structures.

The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.