Attribute Reduction Based On Similarrelations

Rough set theory is a tool to depict incomplete and obscure data, it was at first proposed by Pawlak in1982. The theory can excavate the valuable information from the data effectively. The attribute reduction ofRough Set theory is a research topic with research value and challenging. Attribute reduction can delete theredundant information hidden in data and keep or improve the classification power invariant.Generally, the result of attribute reduction is not only one. We have to find a reduction including lessattributes. The classical attribute reduction model is based on equivalence relations, which is too prodigiouslyrestrictive for many real-valued data. Therefore, the study on more efficient attribute reduction methods andimproving classification precision are the main study directions in rough set theory.Fuzzy set is an generalization of classical set theory to handle data sets with uncertainty. Rough settheory and fuzzy set theory are all set theories handling with fuzzy and unsharp questions. They have meritsand demerits respectively. In fact, they can be complementary to each other when they are used to deal withpractical problems.The thesis discuss a new method for attribute reduction based on similar relations. First, we discussattribute reduction based on similar relations in information systems with no decisions. Then, we propose anew method for attribute reduction based on similar relations in decision systems. We give out the judgementtheorem of attribute reduction and discernible matrix based on similar relations. Furthermore, we study someproperties of attribute reduction based on similar relations. Some practical examples are employed to illustrateour ideas in this thesis. These examples show that the attribute reduction methods discussed in this thesis aremore effective.