Abstract: According to the present theory of Vague soft sets and the relation between fuzzy sets and classical sets, this paper makes definitions of the cut set and nested set of Vague soft sets. Then the paper gives definitions and proofs of the decomposition theorem, representation theorem, extension principle, and their relevant properties of Vague soft sets. Until now the relevance between Vague soft sets and classical soft sets can be found.

Key words: Vague soft sets, decomposition theorem, representation theorem, extension principle

摘要： 基于现有关于Vague软集的研究以及Fuzzy集与经典集合之间的关系，定义了Vague软集截集和集合套的概念。进而给出Vague软集的分解定理、表现定理和扩张原理的定义，以及其相关性质的数学证明。由此构建出Vague软集与经典软集之间的联系。

关键词: Vague软集, 分解定理, 表现定理, 扩张定理