this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

This paper attempts an exposition of the connection between symmetric spaces and hypergroup theory. This connection is not new to those involved in hypergroups, as the classical symmetric spaces have always provided a very rich source of examples for the theory. However for those working in symmetric spaces, the usefulness of the hypergroup point of view may not be well known. It provides a new...

This paper is written in the framework of Special Issue Mathematics entitled “Hypercompositional Algebra and Applications”, focuses on presentation essential principles hypergroup, which prominent structure hypercompositional algebra. In beginning, it reveals structural relation between two fundamental entities abstract algebra, group hypergroup. Next, presents several types hypergroups, derive...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

Wildberger's construction enables us to obtain a hypergroup from random walk on special graph. We will give probability theoretic interpretation products the hypergroup. The can be identified with commutative algebra whose basis is transition matrices. estimate operator norm of such matrix and clarify relationship between their walks.

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthog...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...