Abstract: In this paper，fuzzy quotient space theory is extended to fuzzy λ-quotient space theory，it is proved that a fuzzy equivalence relation given in universe corresponds to a normalized isosceles distance given in λ-quotient space.A series of λ-cut relation can determine only one fuzzy equivalence relation is presented.The definition of λ-fuzzy quotient space is proposed，and its properties are discussed.A group of λ-fuzzy quotient space is introduced to solve fuzzy problem.

Key words: λ-cut relation, λ-quotient space, distance space, fuzzy λ-quotient space, semi-order lattice

摘要： 把模糊商空间理论推广为模糊λ商空间理论，证明论域上的一个模糊等价关系一一对应于λ商空间上的一个归一化等腰距离函数；给定一个λ截关系序列，则唯一确定一个模糊等价关系。给出模糊λ商空间的定义，并讨论其性质，引入模糊λ商空间族来求解模糊问题。

关键词: λ截关系, λ商空间, 距离空间, 模糊λ商空间, 完备格