Knowledge reduction based on the equivalence relations defined on attribute set and its power set |
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Authors: | Ling Wei Hong-Ru Li |
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Affiliation: | a Department of Mathematics, Northwest University, Xi’an, Shaanxi 710069, PR China b Faculty of Science, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China |
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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 Cr and CR are defined, where r and R are equivalence relations defined on the attribute set and its power set, respectively. The properties of Cr and CR are also discussed. The necessary and sufficient condition for Cr=CR is then given and employed to construct an approach to attribute reduction in information systems. It is also proved that under the condition Cr=CR, 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]. |
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Keywords: | Knowledge discovery Information system Equivalence relation Closure operator Closed set Attribute reduction |
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