Approximations in hypergroups and fuzzy hypergroups

AbstractThe first part of this paper represents a continuation of the study of approximations in a hypergroup. We analyse the lower and upper approximations of a subset in a hypergroup, with respect to some operators, particularly the completeness operator. In the last part, we introduce and analyse the lower and upper approximation of a subset in a fuzzy hypergroup

Contributions in Mathematics: Hyperstructures of Professor Thomas Vougiouklis

After presenting some basic notions of hyperstructures and their applications, I shall point out on the contribution of Professor Thomas Vougiouklis to this field of research: algebraic hyperstructures

A Survey on the Theory of <i>n</i>-Hypergroups

This paper presents a series of important results from the theory of n-hypergroups. Connections with binary relations and with lattices are presented. Special attention is paid to the fundamental relation and to the commutative fundamental relation. In particular, join n-spaces are analyzed

FUZZY GRADE OF SOME HYPERGROUPS

One determines the fuzzy grade of a hypergroup of functions and of some hypergroups associated with ordered sets

Redox reactions as experimental examples of ternary weak algebraic hyperstructures

A ternary hyperoperation on a set H is a 3-ary hyperoperation, which associates a subset of H with any three elements of H. In this paper, we give examples of ternary hyperoperations associated with redox reactions. We observe that for Ag, Cu, Am and Au the ternary hyperoperations are weak associative and so their algebraic structures are $H_v$-semigroups

Derived Hyperstructures from Hyperconics

In this paper, we introduce generalized quadratic forms and hyperconics over quotient hyperfields as a generalization of the notion of conics on fields. Conic curves utilized in cryptosystems; in fact the public key cryptosystem is based on the digital signature schemes (DLP) in conic curve groups. We associate some hyperoperations to hyperconics and investigate their properties. At the end, a collection of canonical hypergroups connected to hyperconics is proposed