Discernibility matrix simplification for constructing attribute reducts

  • Authors:

  • Yiyu Yao;Yan Zhao

  • Affiliations:

  • Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

This paper proposes a reduct construction method based on discernibility matrix simplification. The method works in a similar way to the classical Gaussian elimination method for solving a system of linear equations. Elementary matrix simplification operations are introduced. Each operation transforms a matrix into a simpler form. By applying these operations a finite number of times, one can transform a discernibility matrix into one of its minimum (i.e., the simplest) forms. Elements of a minimum discernibility matrix are either the empty set or singleton subsets, in which the union derives a reduct. With respect to an ordering of attributes, which is either computed based on a certain measure of attributes or directly given by a user, two heuristic reduct construction algorithms are presented. One algorithm attempts to exclude unimportant attributes from a reduct, and the other attempts to include important attributes in a reduct.