Abstract: Vague sets theory has gained great attention from more and more researchers for its applications in various fields, fuzzy entropy, similarity measure and distance measure are the most important technologies in Vague sets. Nowadays, several formula about fuzzy entropy, similarity measure and distance measure of Vague sets have been proposed,but all of these researches did not discuss the relations between these measures. This paper based on the axiom definitions of fuzzy entropy, similarity measure and distance measure of Vague sets, gave mutual induced relations between these measures. Complete relations between fuzzy entropy, similarity measure and distance measure were established.

Key words: Vague sets, Fuzzy entropy, Similarity measure, Distance measure