Research On Similarity Measure Of Set Theories With Uncertain Boundaries

Vague Sets Theory proposed by W. L. Gau and D. J. Buehrer, is the development of Fuzzy Sets Theory. In the real world, there exists quite a number of information that is fuzzy but can not be expressed and processed by Fuzzy Sets Theory, while Vague sets can express and handle more fuzzy information. The study of similarity measure of Vague Sets will provide a new tool to pattern recognition.Firstly, a novel similarity measure between Vague Sets is proposed in this paper. Several similarity measures are introduced in the paper, on the basis of which, a novel similarity measure is presented. Compared with the measures of similarity between Vague sets given by present articles,the method is more differentiated, rational and close to people's understanding; Secondly, a new set theory is proposed. Based on the Fuzzy Rough Set theory , combined the Rough sets theory with the Vague sets theory, a new sets theory-Vague Rough sets theory is introduced, some characterizations of this theory are given and proved. This new theory presented in this paper is very important in theory and in practice.Finally, several Set theories with uncertain boundaries ,that is, fuzzy sets, vague sets and rough sets, are discussed. A novelty similarity measure of them is introduced.