Abstract: On the basis of the study on intuitionistic fuzzy relation，this paper proposes the transitivity and the nontions of transitive closure and their properties of intuitonistic fuzzy，and proves the minimum theorem of intuitionistic fuzzy relation.Firstly the transitivity and the nontions of transitive closure of intuitonistic fuzzy are given by using the intuitonistic fuzzy compositional operations and its properties.Secondly，the calculate formulae and some properties of transitive closure are obtained by using the properties of intuitionistic fuzzy relation，with necessary course of proof.Finally，when R is symmetric，a conclusion is drawn that six different intuitionistic fuzzy relations can be constructed at most by using reflexive closure operator，symmetric closure operator and transitive closure operator of an intuitionistic fuzzy relation.

摘要： 在直觉模糊关系再研究的基础上，提出了传递的直觉模糊关系、传递闭包核算子及其性质，得出了直觉模糊关系的极小定理。利用直觉模糊关系合成运算及其性质给出传递的直觉模糊关系、直觉模糊关系的传递闭包算子。利用直觉模糊关系的性质得出了传递闭包的计算公式和性质，并给出必要的证明。当R是对称的，通过自反闭包算子、对称闭包算子、传递闭包算子作用R，可最多得出6个彼此不同的直觉模糊关系。