Abstract: The quotient space theory is extended into intuitionistic fuzzy set theory, and intuitionistic fuzzy quotient space is established. An intuitionistic fuzzy equivalent relation and distance are defined. An elementary theory of intuitionistic fuzzy quotient space based on intuitionistic fuzzy equivalent relation is established. A cluster of intuitionistic fuzzy quotient spaces induced by a cluster of ordered intuitionistic fuzzy equivalent relations constitutes a complete semi-order lattice. 

Key words: quotient space theory, intuitionistic fuzzy distance, intuitionistic fuzzy equivalent relation, intuitionistic fuzzy quotient space

摘要： 把商空间理论推广到直觉模糊集理论中，建立直觉模糊商空间。定义直觉模糊等价关系和直觉模糊距离。建立基于直觉模糊等价关系的商空间基本定理。证明由有序的直觉模糊等价关系簇诱导的直觉模糊商空间构成一个完备半序格。

关键词: 商空间理论, 直觉模糊距离, 直觉模糊等价关系, 直觉模糊商空间