Soft hypergroups and soft hypergroup homomorphism

Abstract

Soft set is a general mathematical tool for dealing with uncertainties and imprecision. Many complicated problems in economics, engineering, environment, social science, medical science and other fields involve uncertain data. These problems cannot be solved using existing classical methods such as fuzzy set theory and rough set theory. Hence the concept of soft sets was introduced as a new mathematical tool for dealing with uncertainties that is free from the difficulties affecting the existing methods. The theory of hyperstructures and hyperalgebra on the other hand, was introduced as an extension of the classical theory of sets as well as the theory of abstract algebra. This theory states that in an algebraic hyperstructure, the composition of two elements is a set. The study of soft hyperstructures which is an extension of the theory of soft sets and the theory of algebraic hyperstructures began with the introduction of the notion of soft hypergroupoids and soft subhypergroupoids. In this paper, we study the theory of soft hyperalgebra by introducing the notion of soft hypergroups and soft subhypergroups as an extension of the notion of soft sets, algebraic hyperstructures and soft hyperstructures. This is followed by the introduction of the notion of soft homomorphism of hypergroups. Furthermore the basic properties and structural characteristics of these notions are studied and discussed.