The Entropy And Similar Measure Of Fuzzy Sets And Vague Set And Their Applications In Pattern Recognition

Since L.A.Zadeh introduced fuzzy sets in 1965,a lot of new theories treating imprecision and uncertainty have been introduced, many kinds of Fuzzy measure methods have been proposed. And these Fuzzy measure methods have found an increasingly wide utilization in the handling of actual Fuzzy information, such as Pattern recognition, medical diagnosis, artificial intelligence etc. Meanwhile, there exists quite a number of information that is fuzzy but can not be expressed and processed by fuzzy sets theory in the real world. To settle the shortage of Fuzzy Sets theory, W.L.Gau and D.J.Buehrer extended the Fuzzy Sets theory, proposed the concepts of Vague Sets, which can express and handle more fuzzy information. The study of similarity measure of Vague Sets will provide a new tool to pattern recognition.Firstly, we introduce the basic concepts of Fuzzy sets, discussing the two important measure methods in Fuzzy measure: fuzzy entropy and distance measure, studying the relationship between fuzzy entropy and distance measure, obtaining some new formulas of distance measure which are induced by entropy and some new formulas of entropy which are induced by distance measure. That is to say, fuzzy entropy and distance measure can be induced by each other. Then we introduce the basic concepts of Vague Sets, using living examples to show that some existing similarity measures are not always suitable for some cases, analyzing the reasons, proposing a new similarity measure based on the axiom definition of similarity measure between Vague sets. Finally, applying this new similarity measure to pattern recognition.