Rough validity, confidence, and coverage of rules in approximation spaces

  • Authors:

  • Anna Gomolińska

  • Affiliations:

  • Department of Mathematics, University of Białystok, Białystok, Poland

  • Venue:
  • Transactions on Rough Sets III
  • Year:
  • 2005

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Abstract

From the granular computing perspective, the existing notions of validity, confidence, and coverage of rules in approximation spaces may be viewed as too crisp since granularity of the space is not, in general, taken into account in their definitions. In this article, an extension of the classical approach to a general rough case is discussed. We introduce and investigate graded validity, confidence, and coverage of rules as examples of rough validity, confidence, and coverage, respectively. The graded notions are based on the concepts of graded meaning of formulas and sets of formulas, studied in our earlier works. Among others, the notions of graded validitity, confidence, and coverage refine and extend the classical forms by taking into account granules of information drawn toward objects of an approximation space.