The Combination And Application Of Rough Sets And Fuzzy Sets

Rough set and fuzzy set apply to research of incomplete, inaccurate problems of knowledge in information systems. The start point of rough set theory solving problems is indiscernible nature knowledge in information systems. Fuzzy set emphasizes the fuzzy nature of set, and utilizes the fuzzy nature of knowledge in information systems. The combination of rough set and fuzzy set form rough fuzzy se t (RF se t) , fuzzy rough se t (FR se t). Based on the research of Pawlak Z, Banerjee U, Pat S K, Nanda S, Huanglin Zeng, the paper inquires into the structure nature, fuzzy-degree, near-degree, membership, algebra nature of RF set (The paper only includes conclusions about RF set, with regard to FR set, please refer to paper that is in t err el a ted).In chapter one, three basic theorem:decomposition theorem, representation theorem, expand theorem are discussed. Furthermore, from the angle of lattice , it researches high-type RF set .In chapter two, first, fuzzy-degree, near-degree of RF set are researched. On the base, we get a new method of attribute reduction. It' s of great help to realize theoretical results in application field. Next, we study the membership of RF set , then pose a new method of information classification. After that, we research T -rough-fuzzy-inclusion and get a new way of attribute evaluation. It' s a base of research in application of RF set .In chapter three, we defines the rough fuzzy number, and research the quality. We can get RF regression by means of combining RF number and regression analysis, which is some use in forecasting.At last, the paper gives two open questions .