In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups neutro-hypergroups). We investigate property anti-semihypergroups anti-hypergroups). also give a new alternative neutro-hyperoperations anti-hyperoperations), neutro-hyperoperation-sophications anti-hypersophications). Moreover, show that these concepts are different from classical by several e...

In this paper, we introduce the concept of topological ?-semihypergroups as a generalization semihypergroups and semigroups. Also, present new connection between by special equivalence relation. Moreover, define consider quotient maps homomorphisms on ?-semihypergroups.

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.

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...

Relations between rough sets and algebraic structures have been already considered by many mathematicians. Motivated by studying the properties of rough (m,n) bi-Γ -hyperideals in Γ -semihypergroups, we now introduced the notion of prime (m,n) biΓ -hyperideals in Γ -semihypergroups and investigated several properties of these prime (m,n) bi-Γ -hyperideals. Also we applied the rough set theory t...

The aim of this research work is to define a new class hyperstructure as generalization semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, fundamental relation on (Δ,G)-sets prove some results in respect. Then, introduce the notions quotient by using congruence relations. Finally, concept complete parts Noetherian(Artinian)

One from classical constructions of algebraic binary hyperstructures (semihypergroups and hypergroups) from ordered algebraic systems is based on a certain Lemma on principal ends generated by products of pairs of elements – shortly termed as Ends-Lemma. First version of this auxiliary lemma was obtained in the monography [3]. The mentioned lemma is applied not only in case of hyperstructures c...

In a previous paper [1], we initiated systematic study of semihypergroups and had thorough discussion about some important analytic algebraic objects associated to this class objects. paper, investigate free structures on the category semihypergroups. We show that natural product structure along with topology, although fails give for topological groups, works well vast non-trivial ‘pure’ contai...