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.

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 weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

Let S be a semigroup and f be a mapping of S into the class of nonzero cardinal numbers. The mapping f is said to be representable if there exist a groupoid G and a homomorphism h of G onto S such that Ker(h) is the least congruence of G for which the corresponding factor is a semigroup and f(a) = Cardh(a) for all a ∈ S. The investigation of representable mappings (see the papers [2] and [3]) i...

Hyperstructure theory was born in 1934 when Marty [9] defined hypergroups, began to analyze their properties and applied them to groups, rational algebraic functions. Now they are widely studied from theoretical point of view and for their applications to many subjects of pure and applied properties. In 1986, Sen and Saha [12] introduced the concept of Γsemigroup as a generalization of semigrou...

A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt m...

The notion of (m,n)-ideals of semigroups was introduced by Lajos [13, 14]. Later (m,n) quasi-ideals and (m,n) bi-ideals and generalized (m,n) bi-ideals were studied in various algebraic structures. The notion of a rough set was originally proposed by Pawlak [16] as a formal tool for modeling and processing incomplete information in information systems. Some authors have studied the algebraic pr...

In this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.We also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.