| In this thesis, some properties and structures of module based on thetheories of modules are studied by means of fuzzy set theory and fuzzy soft set theory.The whole paper is composed of three chapters.In the first chapter, we provide a sketch of the historical situation and the presentdevelopment of relevant subjects about fuzzy algebras, fuzzy soft algebras andmodules as well as the main work done in this paper. Also, some preliminaries onmodules, fuzzy binary operations and fuzzy soft sets are given.In the second chapter, combining modules with fuzzy binary, we study thecharacterizations and structures of a kind of new fuzzy modules. In particular,three isomorphism theorems of fuzzy modules are proved.In the third chapter, we continute to investigate several kinds of particularmodules through fuzzy soft set theory, such as (∈_γ,∈_γ∨q_δ) fuzzy soft left (orright) R submodules,(∈_γ,∈_γ∨q_δ) fuzzy soft (R, S) bi submodulesand (∈_γ,∈_γ∨q_δ) fuzzy soft∨q_δuasi submodules. Finally, we put forward theconcept of regular modules and study the relation among regular module andsome kinds of submodules mentioned above. |
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