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

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