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

  • Authors:
  • Ling Wei;Hong-Ru Li;Wen-Xiu Zhang

  • Affiliations:
  • Department of Mathematics, Northwest University, Xi'an, Shaanxi 710069, PR China and Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China;Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China;Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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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 C"r and C"R are defined, where r and R are equivalence relations defined on the attribute set and its power set, respectively. The properties of C"r and C"R are also discussed. The necessary and sufficient condition for C"r=C"R is then given and employed to construct an approach to attribute reduction in information systems. It is also proved that under the condition C"r=C"R, 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].