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.

This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion (softly) left regularity, right intra-regularity, complete generalized regularity investigate their related properties. Several characterizations them in terms provided. Finally, relationships betwee...

In this paper, 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 $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

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 ...

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...

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.