In this paper, we introduce a path hyperoperation associated with a hypergraph,which is an extension of the Corsini’s hyperoperation.We investigate some related properties and study relations betweenthe path hyperoperation and hypergraph theory.

‎In this paper‎, ‎first‎, ‎we show how to define an algebraic hyperstructure by using algorithms‎. ‎Then‎, ‎we present algorithms that calculate specific elements in algebraic hyperstructures‎. ‎These specific elements are‎: ‎scalars‎, ‎scalar identities‎, ‎identities‎, ‎inverses‎, ‎zero elements‎, ‎right simplifiable elements‎, ‎left simplifiable elements‎, ‎left absorbing-like elements and right absorbing-like elements‎. ‎We also introduce some algorithms in algebraic hyperstructures to check properties or calculate specific members‎. ‎These algorithms are presented for algebraic hyperstructures with one hyperoperation‎, ‎i.e‎. ‎hypergroupoids‎. ‎However‎, ‎they can be developed for other algebraic hyperstructures‎.

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 helix-hyperoperations, hyper-sum and hyperproduct, are defined on any type of ordinary matrices. Thus, they overcome restrictions which ordinary sum and product on matrices have. We focus on the representation theory of hyperstructures, where the helix-product on any type of matrices, can be used. In fact, the helixproduct gives a hyper- semi-hypergroup structure or its generalization the Hv-semigroup. We restrict on the case of two m × n, with m < n, matrices, cases. The crucial point is that all entries of the original matrices are used, so the helix-product do not lose any information. For the case of n × (n + 1) we present subsets closed under the helix-product. Finite or infinite fields and Hv- fields, are used, as well.

‎‎‎In this paper first we introduce right(resp‎. ‎left) induced hyperlattices and investigate some of their properties‎. ‎Especially‎ ‎a characterization of the smallest strongly regular relation for the class of distributive right/left induced hyperlattice is investigated‎. ‎Next we propose and study the generated hyperlattices from hyperlattices‎. ‎Finally‎, ‎the right induced hyperlattices of two Boolean lattices of four DNA bases and physico-chemical properties of amino acids of four DNA bases are investigated‎.

‎‎‎In this paper first we introduce right(resp‎. ‎left) induced hyperlattices and investigate some of their properties‎. ‎Especially‎ ‎a characterization of the smallest strongly regular relation for the class of distributive right/left induced hyperlattice is investigated‎. ‎Next we propose and study the generated hyperlattices from hyperlattices‎. ‎Finally‎, ‎the right induced hyperlattices of two Boolean lattices of four DNA bases and physico-chemical properties of amino acids of four DNA bases are investigated‎.

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 research, we introduce fundamental hypergroups and dependent hypergroups then we investigate a connection between hypergroup theory and nuclear physics and fundamental particles. We show that interaction process such as Lepton actions in fundamental particle physics and nuclear fusion Stars forms a fundamental hypergroup.

In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated.