Rough Set Theory Model

At present, rough set theories are being widely applied in Data Mining and Knowledge Discovery in Database. According to present researches, continuous generalization studies for rough set model will be done in this paper. It mainly adopts the formation ways and associates with these uncertainty theories of probability, fuzzy set, random set, set pair analysis and vague set which are referred to as follows:(1) Rough approximation operators are proposed by the opposite of a matter in probability theories. It is an improvement for probability ( I ) rough set model.(2) Under the concept of fuzzy neighborhood operators, rough approximation operators on dual universes are introduced. Then, the mistake classification rate between two fuzzy sets is defined. Later, fuzzy variable precision rough set model is proposed based on the two definitions.(3) Fuzzy rough set model based on random set on dual universes is proposed. It gives a way to deal with the uncertainty problems that knowledge in knowledgebase is fuzzy and gained by random reasons, and the described object is also fuzzy.(4) On the one hand, a new idea of set pair connection degree is proposed based on the number of elements of the given sets. Moreover, fuzzy set pair connection degree is defined. Lastly, the two ideas are introduced to rough set theories, which induces new set pair rough set model and fuzzy set pair rough set model.(5) In this paper, the concept of vague cut-set is introduced. Then, rough vague approximation operators and vague rough approximation operators are defined based on the two theories of rough set and vague set.(6) According to the definition of intuitionistic L-fuzzy set proposed by K.Atanassov, intuitionistic L-fuzzy rough set is introduced. Furthermore, it is proved that vague rough set introduced before is actually an intuitionistic L-fuzzy rough set.