Similarity Measures And Attribute Reduction In Rough Set Theory

Rough set theory is a kind of new soft computing tool, it can e?ectively deal withvagueness and uncertainty data, and then discover the implicit knowledge. It was pro-posed by Polish professor Pawlak in 1982. Because of its advantages on novel idea,simple calculation and unique method, it has become an important kind of informationprocessing technology. Nowdays more and more scholars pay attention to this theory.Similarity measure is a powerful tool to compare two objects of similar degree. Sohow to define more reasonable and accurate similar degree of two objects has become oneof the hot research problems. This dissertation defines two kinds of similarity measuresbetween two rough sets. The first one is based on the upper and lower approximations.According to di?erent requirements, di?erent weights are assigned to the upper and lowerapproximation respectively. Thus it maybe have more flexibility in applications. Sincea kind of inclusion degree can define a similar degree, this dissertation use inclusiondegree to define another similarity measure between two rough sets. The dissertationalso discusses the two similarity measures in the case of rough fuzzy set and intuitionisticfuzzy rough set.Attribute reduction is one of the core problem in rough set theory. Through at-tribute reduction we can delete redundant information and get a relatively simple andaccurate classification. By employing the proposed similarity measures, this dissertationdefines two novel importances of attribute. An algorithm for attribute reduction of aninformation system is also formulated.