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)

We consider a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined as follows: a P ∨ b = a ∨ b ∨ P , a Q ∧ b = a ∧ b ∧Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. We explore some properties of (L, P ∨, Q ∧) with special attention to various types of P ∨ and Q ∧ distributivity. AMS Subjec...

Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a s...

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...

This paper is written to give an overview of past, ongoing and future work in the area of hypertext and programming environments at Aalborg University. In the past, the main emphasis of our work has been on data modeling and storage aspects of hypertext. Our current research focuses more directly at programming environments. Our hypothesis is that the node-link representation, inspired by hyper...

The combination of two elements in a group structure is an element, while, hypergroup, the non-empty set. use hypergroups appears mainly certain subclasses. For instance, polygroups, which are special subcategory hypergroups, used many branches mathematics and basic sciences. On other hand, multi-fuzzy set, element universal set may occur more than once with possibly same or different membershi...

In the classical theory of probability we start by a pair (Ω, ), with Ω set of elementary events and σ-algebra of subsets of Ω, called events. A probability on is defined as a countable additive and positive function p such that p(Ω)=1. If A and B are two events, the conditional probability p(A/B) is defined if and only if p(B) is not null, by considering the quotient p(AB)/p(B). In the theory ...