On fundamental isomorphism theorems in soft subgroups

Abstract

Molodsov initiated a novel concept of soft set theory, which is a completely new approach for modeling vagueness and uncertainty, which there is no limited condition to description of objects and is free from the difficulties affecting existing methods. This makes the theory very convenient and easy to apply in practice. After the pioneering work of Molodsov, there has been a great effort to obtain soft set analogues of classical theories. Among other fields, a progressive developments are made in the field of algebraic structure. To extend the soft set in group theory, many researchers introduced the notions of soft subgroup and investigated its applications in group theory and decision making. In this paper, by using the soft sets and their duality, we introduce new concepts on the soft sets, which are called soft quotient subgroup and quotient dual soft subgroup. We then derive their algebraic properties and, in sequel, investigate the fundamental isomorphism theorems in soft subgroups analogous to the group theory.