Abstract: The concepts of degree of truth-compatibility, degree of false-compatibility degree of truth-equality, degree of falscequality based on t-norm and t-conorm were introduced, because a vague set has the characteristic of truth-membership function and fase-membership function. Futhermore we presented the concepts of semi-vague partitions and vague partitions by using locically degree of truth-compatibility, degree of false-compatibility degree of truth-equality,degree of falscequality, and we investigated the characters of semi-vague partitions and vague partitions.

Key words: t-norm,t-conorm,Semi-vague partion,Vague partion