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Definability and Other Properties of Approximations for Generalized Indiscernibility Relations

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Transactions on Rough Sets XI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5946))

Abstract

In this paper we consider a generalization of the indiscernibility relation, i.e., a relation R that is not necessarily reflexive, symmetric, or transitive. On the basis of granules, defined by R, we introduce the idea of definability. We study 28 basic definitions of approximations, two approximations are introduced for the first time. Furthermore, we introduce additional 8 new approximations. Our main objective is to study definability and coalescence of approximations. We study definability of all 28 basic approximations for reflexive, symmetric, and transitive relations. In particular, for reflexive relations, the set of 28 approximations is reduced, in general, to the set of 16 approximations.

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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. Grzymala-Busse

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

    Jerzy W. Grzymala-Busse

  3. Department of Computer Science, University of Rzeszow, 35–310, Rzeszow, Poland

    Wojciech Rza̧sa

Authors
  1. Jerzy W. Grzymala-Busse
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  2. Wojciech Rza̧sa
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Editors and Affiliations

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

    James F. Peters

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

    Andrzej Skowron

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Grzymala-Busse, J.W., Rza̧sa, W. (2010). Definability and Other Properties of Approximations for Generalized Indiscernibility Relations. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XI. Lecture Notes in Computer Science, vol 5946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11479-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-11479-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11478-6

  • Online ISBN: 978-3-642-11479-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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