【摘要】 本文利用商空间理论中的粒度和层次概念来讨论模糊子集的结构和性质.首先将基于等价关系的商空间理论推广到基于模糊相容关系,接着讨论模糊相容关系的同构性及同构性的判别问题,最后利用模糊相容关系定义模糊子集,并讨论其性质.主要给出以下结果:(1)模糊相容关系的几种等价表示形式;(2)模糊相容关系的同构定义;(3)模糊相容关系同构的判别准则;(4)模糊相容关系下的模糊子集的定义及其相关性质;以及(5)模糊子集同构的充分必要条件.这些结果加深了我们对模糊相容关系和模糊集的理解.更多还原

【Abstract】 The structure and characteristic of fuzzy subsets are discussed by using the concepts of granulation and hierarchy in quotient space theory.First,the equivalence relation based quotient space theory is extended to the fuzzy tolerance relation.Second,the isomorphism and its discriminant of fuzzy tolerance relations are discussed.Finally,by using the fuzzy tolerance relation to define the fuzzy subset,its properties are addressed. The main results are given below:(1) several equivalent statements of fuzzy tolerance relations;(2) the definition of isomorphism of fuzzy tolerance relations;(3) the isomorphic discriminant of fuzzy tolerance relations;(4) the definition and properties of fuzzy subsets based on the fuzzy tolerance relations;and(5) the necessary and sucient condition of the isomorphism of fuzzy subsets.These results will help us further comprehend the concepts of fuzzy tolerance relations and fuzzy subsets.更多还原