Method, Model and Application for the Conversion from Vague Sets to Fuzzy Sets

Abstract

Both Vague sets theory and Fuzzy sets theory were often used to handle fuzzy information. The two theories had their own merits and demerits. Using fuzzy sets theory, the nonlinear mapping relationship of the fuzzy system could be depicted much better by changing (except ¿ = 1 and p = 1, which become linear model) ¿ (optimization criterion parameter) and p (distance parameter), although only two kinds of information, including support grade and opposition grade of an object could be expressed by the membership function Using Vague sets theory, three kinds of information, which include support grade, opposition grade and hesitate grade¿neither support nor oppose¿of an object could be expressed by using the membership function, but most of the similarity measure models between Vague sets were linear, so some disadvantages exist in them. In this paper, the Vague-Fuzzy sets theory was founded, this method could enhance the capacity of treating fuzzy information by combining the bigger capacity of Vague sets to express the uncertainty with the better ability of Fuzzy sets to depict the characteristics of nonlinear mapping relationship. The method was as follows: firstly, on the basis of studying the method of assessing the vague values of the index, the method and model of conversing Vague sets into Fuzzy sets were established, and the fuzzy pattern recognition model was established with multiplayer; then, taking the approximate translating result computed by the conversion model as the input of the fuzzy pattern recognition model, the multi-evaluation model was founded; finally, taking the city classification of Jinan as an example, the results of case studies of the model established show that the method is scientific and practical.