The aim of this paper is the study of fuzzy $Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $Gamma$-hyperring under a certain conditions is two-valued.Finally,...

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

Over the years, different types of hyperideals have been introduced in order to let us fully realize structures hyperrings general. The aim this research work is define and characterize a new class Krasner $(m,n)$-hyperring that we call n-ary $J$-hyperideals. A proper hyperideal $Q$ with scalar identity $1_R$ said be an $J$-hyperideal if whenever $x_1^n \in R$ such $g(x_1^n) Q$ $x_i \notin J_{(...

The notion of bipolar fuzzy set was initiated by Lee (2000) as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study on bipolar ( ,   )-fuzzy sets in -semihypergroups. By using the concept of bipolar ( ,   )-fuzzy sets (Yaqoob and Ansari, 2013), we introduce the ...

Let G be a group (monoid) with identity e and R commutative Krasner hyperring. In this paper, we introduce the concepts of graded absorbing hyperideals hyperring such as, 2-absorbing hyperideals, n-absorbing subhypermodules. Some basic properties these structures characterizations homogeneous components are proved.

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.

We introduce the notions of soft hyperrings, idealistic soft hyperrings, soft subhyperrings and soft hyperideals, and discuss some related properties. Moreover, we establish three (fuzzy) isomorphism theorems of soft hyperrings.

In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.