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Generalized Parameterized Approximations

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Rough Sets and Knowledge Technology (RSKT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6954))

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Abstract

We study generalized parameterized approximations, defined using both rough set theory and probability theory. The main objective is to study, for a given subset of the universe U, all such parameterized approximations, i.e., for all parameter values. For an approximation space (U, R), where R is an equivalence relation, there is only one type of such parameterized approximations. For an approximation space (U, R), where R is an arbitrary binary relation, three types of parameterized approximations are introduced in this paper: singleton, subset and concept. We show that the number of parameterized approximations of given type is not greater than the cardinality of U. Additionally, we show that singleton parameterized approximations are not useful for data mining, since such approximations, in general, are not even locally definable.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS, 66045, USA

    Jerzy W. Grzymała-Busse

  2. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

Authors
  1. Jerzy W. Grzymała-Busse
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, S4S 0A2, Saskatchewan, Canada

    JingTao Yao

  2. Department of Applied Computer Science, University of Winnipeg, R3B 2E9, Winnipeg, Canada

    Sheela Ramanna

  3. Institute of Computer Science & Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, P.R. China

    Guoyin Wang

  4. Chair of Computer Science, University of Rzeszów, Poland

    Zbigniew Suraj

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Grzymała-Busse, J.W. (2011). Generalized Parameterized Approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_20

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  • DOI: https://doi.org/10.1007/978-3-642-24425-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24424-7

  • Online ISBN: 978-3-642-24425-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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