In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of(R,S)-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
