Rough Set Theory Model

At present, rough set theories are being widely applied in Data Mining and Knowledge Discovery in Database. According to the present researches for rough set model, continuous generalization studies for Pawlak rough set model will be done in this paper. It mainly adopts the formation ways and associates with these uncertainty theories of fuzzy set, set pair analysis and vague set which are referred to as follows:(1) Variable precision Bayesian rough set model is just suitable for complete information system. As for the limitation, variable precision Bayesian rough set model based on set pair analysis is proposed by introducing the concept of set pair analysis, which extends the model to incomplete information system. And a theorem equivalent to the definition of model is given. When we regulate the similarity and precision of model, knowledge of various similarities and precisions on the concept X is obtained. Thus we will further know information of the database.(2) In present, there exist several extensions in incomplete information system, such as extensions based on tolerance relation and similarity relation, etc. However, these extensions have their own limitations. As for the limitations, set-pair variable precision rough set model based on limited tolerance relation is proposed by introducing the concept of relatively classified fault rate. Thus the classical rough set model and set-pair rough set model based on limited tolerance relation are extended. Also some properties about the upper and lower approximation operators of the model are discussed. Finally, by an example, it is verified that the model is feasible and effective to deal with vagueness and uncertainty in incomplete information system.(3) The decomposition theorem in vague sets is given by the concept of the cut in vague sets. Meanwhile, a rough approximation operator in the vague environment is defined by a vague relation proposed by us, which extends fuzzy rough approximation operators in the fuzzy relation. Also some properties of operators of the model are discussed. The representations of vague rough approximation operators are presented. Thus vague set theory is not only applied but extended to rough set theory.