Certain fuzzy version of soft structures on soft g-modules

Abstract

In this paper, we introduce two kinds of G-modules of a vector space with respect to soft structures, which are intersection fuzzy soft G-modules (IFSG-module) and union fuzzy soft G-module (UFSG-module). These new concepts show that how a soft set affects on a G-module of a vector space in the mean of intersection, union and inclusion of sets and thus, they can be regarded as a bridge among classical sets, fuzzy soft sets and vector spaces. We then investigate their related properties with respect to soft set operations, soft image, soft pre-image, soft anti image, α-inclusion of fuzzy soft sets and linear transformations of the vector spaces. Furthermore, we obtain the relation between IFSG- modules and UFSG-modules and give the applications of these new G-modules on vector spaces.