Game-Theoretic Rough Sets

  • Authors:

  • Joseph P. Herbert;Jingtao Yao

  • Affiliations:

  • (Correspd.) Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada. herbertj@cs.uregina.ca/ jtyao@cs.uregina.ca;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada. herbertj@cs.uregina.ca/ jtyao@cs.uregina.ca

  • Venue:
  • Fundamenta Informaticae - Advances in Rough Set Theory
  • Year:
  • 2011

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Abstract

This article investigates the Game-theoretic Rough Set (GTRS) model and its capability of analyzing a major decision problem evident in existing probabilistic rough set models. A major challenge in the application of probabilistic rough set models is their inability to formulate a method of decreasing the size of the boundary region through further explorations of the data. To decrease the size of this region, objects must be moved to either the positive or negative regions. Game theory allows a solution to this decision problem by having the regions compete or cooperate with each other in order to find which is best fit to be selected for the move. There are two approaches discussed in this article. First, the region parameters that define the minimum conditional probabilities for region inclusion can either compete or cooperate in order to increase their size. The second approach is formulated by having classification approximation measures compete against each other. We formulate a learning method using the GTRS model that repeatedly analyzes payoff tables created from approximation measures and modified conditional risk strategies to calculate parameter values.