Extended Model And Attributes Reduction Of Rough Set To Incomplete Information Systems

Rough set theory, proposed by Pawlak in the early 1980s, is a mathematical theory for reasoning about data. The main idea of the theory is to approximate inexact, uncertain concepts by using of available knowledge or information. Since 1990s, it has attracted much attention of researchers around the world, and has been well developed and applied. Now, this theory has become a flash point in the research area of computer science and information science.In classical Rough Set, the equivalence relations play important roles. In fact, the equivalence relations are likely to inexistence in practice, so the classical rough set theory is limited in incomplete information systems. For example, because of null value, the equivalence relations aren't constructed via attributes value. The kind of binary relation is basis for rough compute, attributes reduction and extract rules in incomplete information systems.Started with the equivalence relations of classical rough set model, we put forward four kinds of extensions rough set model by introduceding majority inclusion relation. Not only does the extension reserve the advantages of the present model, but also these models discard the disadvantages of the present model.The paper introduces some new concepts of knowledge reduction based on variable precision rough set theory such as upper distribution reduction and lower distribution reduction. And their relationships are discussed. The judgement theorems with respect to upper and lower reductions are obtained. So one can calculates the reductions by the discernibility formulas in incomplete systems.