The aim of this paper is the study of fuzzy Γ-hyperrings. In this regard the notion of ν-fuzzy hyperideals of Γ-hyperrings are introduced and basic properties of them are investigated. In particular, the representation theorem for ν-fuzzy hyperideals are given and it is shown that the image of a ν-fuzzy hyperideal of a Γ-hyperring under a certain conditions is two-valued. Finally, the product o...

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space A d S 3 , which are defined as intersection of projective model with a convex polyhedron RP whose vertices all outside and edges meet . show that uniquely determined by their combinatorics dihedral angles, well induced metric on boundary together an additional combinatorial data, describe possible angles metrics boundary.

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...

Let P be a (non necessarily convex) embedded polyhedron in R, with its vertices on an ellipsoid. Suppose that the interior of P can be decomposed into convex polytopes without adding any vertex. Then P is infinitesimally rigid. More generally, let P be a polyhedron bounding a domain which is the union of polytopes C1, · · · , Cn with disjoint interiors, whose vertices are the vertices of P . Su...

1 Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320 Pakistan 2 The Foundation Department Sur University College P.O. Box 440 P.C 411, Sur, Muscat, Sultanate of Oman Abstract: The concept of quasi-coincidence of fuzzy point with a fuzzy subset has considered. By using this idea, the notion of (, )-fuzzy hyperideal in a semihyperring introduced and consequently, a generalizat...

In this paper, we introduce a generalized class of an Hv-semigroup obtained from an LA-semigroup H. This generalized Hv-structure is called an Hv-LA-semigroup. We provide several examples of Hv-LA-semigroups. Moreover, with the help of an example we obtain that each LA-semigroup endowed with an equivalence relation can induce an Hv-LA-semigroup. We also investigate isomorphism theorems with the...

The concept of quasi-coincidence of interval valued fuzzy point with an interval valued fuzzy subset has considered. By using this idea, the notion of interval valued (α, β)-fuzzy hyperideal in a semihyperring introduced and consequently, a generalization of interval valued fuzzy hyperideals and interval valued fuzzy hyperideals have defined. In this paper, we study the related properties of th...

Inspired by the concept of regular local rings in classical algebra, this article we initiate study parameter elements a commutative Noetherian hyperring. These provide deep connection between dimension hyperring and its primary hyperideals. Then, our focusses on R, with maximal hyperideal M, having property that R is equal to vectorial hyperspace MM2 over hyperfield RM. Finally, using hyperrin...

We investigate the rigidity of hyperbolic cone metrics on 3-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyperideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is d...

In this paper we introduce and analyze the notion of fuzzy hyperideal of a fuzzy hyperring. Then we investigate some properties based on homomorphisms between fuzzy hyperrings. Also, we try to extend the notion of cuts in fuzzy structures for fuzzy hyperrings. We study the quotient structure of a fuzzy hyperring and also we define fuzzy hypercongruences. Then we investigate some connections bet...