Research on Similarity Measures between Vague Sets

Many AI researchers have intensively investigated fuzzy knowledge acquisition. It is considered as a key problem in the fields of expert system, decision analysis, machine learning, ect. We notice that the vague set theory introduced by Gau and Buehrer has been conceived as a new efficient tool to deal with ambiguous data and it has been applied successfully in different fields. A vague set, as a generalization of the concept of fuzzy set, is a set of decision objects, each of which has a grade of membership whose value is a continuous subinterval of [0,1]. It is characterized by a truth-membership function and a false- membership function. In this paper, we analyze the similarity measures between vague sets given in literature. The concept of similarity degree is given. Then we revise them and propose a new kind of similarity measures. The new measures are more rational, thus providing a more useful way to measure the degree of similarity between vague sets.