Certain Double Action on Bipolar Fuzzy Soft G-Modules

Abstract

In this paper, we apply the notion of bipolar-valued fuzzy soft set to module theory. We introduce the concept of bipolar fuzzy soft G-modules, fuzzy soft d-ideals of modules and investigate several properties. We give relations between a bipolar fuzzy soft G-modules and bipolar fuzzy soft d-ideal. We provide a condition for bipolar fuzzy soft G-modules to be a bipolar fuzzy soft d-ideal. We also give characterizations of bipolar fuzzy soft ideal. We consider the concept of strongest bipolar fuzzy relations on bipolar fuzzy soft d-ideals of a module and discuss some related properties.