Introduction to linear representations of soft groups

Abstract

Abstract

Soft set theory originated by Molodtsov is an effective technique for dealing with uncertainties. In the framework of soft set theory, soft group is a key concept of algebraic theory of soft sets. The aim of this paper is provided an initial study of the linear representations of soft groups. The fundamental notions such as linear and matrix representations, equivalent representation, faithful representation, trivial representation of soft groups together with some illustrative examples are introduced. The concepts of soft invariant space, irreducible representation, completely reducible representation are proposed. And then the relationships among these concepts are demonstrated by means of several related theorems.