Abstract: By the definition of Vague values——the elements in the closed subinterval set of the unit interval [0，1]，some new definitions of binary Vague relations，operations of relations，inverse relations，compositional operations and λ-cut relations are introduced.In terms of the concept of ordering relations of interval numbers based on probability，as well as the practical sense of vote models of Vague sets，the definition of a partial ordering relation of Vague values in the closed subinterval set is given，with which we provide the necessary proofs of some primary properties of Vague relations.The definitions of Vague similarity relations with sup-min transitivity and Vague partitions are given，and a one-to-one correspondence between Vague similarity relations and Vague partitions is established.Furthermore，by means of the generalized “and” logic operator based on the continuous triangle norm on unit interval，the new concepts of the particular case of Vague similarity relations——Vague T-similarity relations with T-transitivity and Vague T-partitions are introduced.

Key words: Vague relations, Vague value, partial ordering relation, Vague similarity relations, Vague partitions

摘要： 通过对单位区间[0，1]的闭子区间集中的元素——Vague值的定义，引入二元Vague关系、关系运算、逆关系、关系的合成、λ-截关系等新的定义。从基于可能度的区间数序关系的概念以及Vague集投票模型的实际意义两个方面，引入闭子区间集中Vague值的偏序关系的定义，并利用偏序关系证明了Vague关系的一些主要性质。给出了满足sup-min传递性的Vague相似关系以及Vague划分的定义，建立了Vague相似关系与Vague划分一一对应性，进而以[0，1]上连续t模作为广义的“与”逻辑算子，引入Vague相似关系的特例——满足T-传递性的Vague T-相似关系与Vague T-划分新的定义。

关键词: Vague关系, Vague值, 偏序关系, Vague相似关系, Vague划分