In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

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.

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 SH and TH , respectively. It is shown that TH = SH if and only if β = β ∗. We also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

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 ...

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 objective of this paper is to study neutrosophic hypercompositional structures ( ) H I  arising from the hypercompositions derived from the binary relations τ on a neutrosophic set ( ) H I . We give the characterizations of τ that make ( ) H I  hypergroupoids,quasihypergroups, semihypergroups, neutrosophic hypergroupoids, neutrosophic quasihypergroups, neutrosophic semihypergroups and neu...