Knowledge reduction based on the equivalence relations defined on attribute set and its power set

Abstract: One of the key problems of knowledge discovery is knowledge reduction. This paper proposes a new method for knowledge reduction in information systems. First, two families of closed sets and are defined, where r and R are equivalence relations defined on the attribute set and its power set, respectively. The properties of and are also discussed. The necessary and sufficient condition for is then given and employed to construct an approach to attribute reduction in information systems. It is also proved that under the condition , the proposed approach to knowledge reduction is equivalent to the well-accepted one in reference [W.X. Zhang, Y. Leung, W.Z. Wu, Information Systems and Knowledge Discovery, Science Publishing Company, Beijing, 2003]. [Copyright &y& Elsevier]