Molodtsov introduced the concept of soft set theory, which can be seen and used as a new mathematical tool for dealing with uncertainly. In this paper we introduce and initiate the study of soft m-ary semihypergroups by using the soft set theory. The notions of soft m-ary semihypergroups, soft m-ary subsemihypergroups, soft j-hyperideals, soft hyperideals, soft quasi-hyperideals and soft bi-hyp...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The sets was created as useful mechanism portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of sets. We present notion ordered semihypergroups define hyperideals (bi-hyperideals, quasi hyperideals) an semihypergroup. R...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

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...

Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.

In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. We also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-...