| Most of the problems in economics, engineering, medical science, environments etc. have various uncertainties. To solve these uncertainties, we cannot successfully use classical mathematical methods because of various uncertainties typical for the those problems. In 1999, D.Molodtsov introduced the concept of soft sets,which can be seen as a new mathematical tool as same as fuzzy sets and rough sets for dealing with various uncertainties. Many researchers applied soft set theory to algebras, information science and computing science,and obtained some important results.This paper mainly studied some aspects of soft module.First, the paper introduces the defnition of soft set, fuzzy soft set, rough set and rough fuzzy set. Some basic properties of them are given. Next, we study soft modules based on soft set theory and module theory in this paper. By concepts of soft modules, some examples are illustrated, and some properties of soft modules are given. In particular, the notions of soft homomorphisms and soft isomorphisms are proposed, and three basic soft isomorphism theorems are established. Then we consider the soft exactness of soft modules and some of their properties are discussed. The concept of fuzzy soft modules and fuzzy soft submodules are introduced, and their properties are discussed, some examples are illustrated. Furthermore, the definition of fuzzy soft exactness are given, some of their properties are discussed. The concept of rough soft modules and soft rough modules are introduced, and their properties are discussed. |
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