Abstract: This paper revises two equivalent narratives in the fuzzy quotient space and expands them into three.Then it refines the fuzzy λ-quotient space by making use of the distance function of quotient space X(λ)，which more directly inherits the fuzzy quotient space theory.The information quantity of fuzzy-rough probability approximation space is extended to the one of fuzzy λ-quotient space.And this paper gives the reduction rules of hybrid decision system based on fuzzy λ-quotient space so that fuzzy λ-quotient space can get the same reduction results as fuzzy-rough set.These rules solve the problems that in a traditional rough set model direct discretization of numerical attribute usually brings information loss and fuzzy attributes are not taken into consideration.

Key words: fuzzy equivalence relation, distance space, fuzzy λ-quotient space, hybrid decision system, attribute reduction

摘要： 把模糊商空间中的两个等价的叙述修正并扩展为三个，利用商空间X(λ)的距离函数重新定义了模糊λ商空间，更加直接地继承了模糊商空间理论。把模糊粗糙近似空间的信息量拓展到模糊λ商空间，给出了模糊λ商空间下的混合决策系统约简条件，使模糊粗糙集的属性约简在模糊λ商空间下同样能实现，解决传统粗糙集对连续属性直接离散化容易造成信息缺失和不能对模糊属性处理的问题。

关键词: 模糊等价关系, 距离空间, 模糊λ商空间, 混合决策系统, 属性约简