This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the "sum" of two elements is a subset of the structure. The results in this paper show that these structures .cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and...

Hyperstructures and binary relations have been studied by many researchers, for instance, Chvalina 1, 2 , Corsini and Leoreanu 3 , Feng 4 , Hort 5 , Rosenberg 6 , Spartalis 7 , and so on. A partial hypergroupoid 〈H, ∗〉 is a nonempty setH with a function fromH×H to the set of subsets of H. A hypergroupoid is a nonempty set H, endowed with a hyperoperation, that is, a function fromH ×H to P H , t...

on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

This paper is the results of the ideas suggested by P. Corsini in his paper [10]. Our investigations take in account the paper [13] of I. Cristea. We study the hypergroup generated by the cosets modulo a subgroup (normal subgroup). We prove that (G/H, ◦4) is a complete hypergroup. We take many particular examples to illustrate some known results on hypergroups. Keyword: fuzzy sets, hypergroups,...

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...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Krasner hyperrings are a generalization of rings. Indeed, in hyperring the addition is hyperoperation, while multiplication an ordinary operation. On other hand, rough set theory near theory. Now, this paper we interested combining these concepts. We study and investigate notion on nearness approximation space. Also, define subhyperring, hyperideal, homomorphism prove some results present sever...

A neutrosophic hyperstructure is an algebraic structure generated by a given hyperstructure H and an indeterminacy factor I under the hyperoperation(s) of H. The objective of this paper is to study canonical hypergroups and hyperrings in which addition and multiplication are hyperoperations in a neutrosophic environment. Some basic properties of neutrosophic canonical hypergroups and neutrosoph...