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Rough Validity, Confidence, and Coverage of Rules in Approximation Spaces

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Transactions on Rough Sets III

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3400))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Białystok, Akademicka 2, 15267, Białystok, Poland

    Anna Gomolińska

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  1. Anna Gomolińska
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Gomolińska, A. (2005). Rough Validity, Confidence, and Coverage of Rules in Approximation Spaces. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets III. Lecture Notes in Computer Science, vol 3400. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427834_3

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  • DOI: https://doi.org/10.1007/11427834_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25998-5

  • Online ISBN: 978-3-540-31850-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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