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Information Granulation and Approximation in a Decision-Theoretical Model of Rough Sets

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Rough-Neural Computing

Part of the book series: Cognitive Technologies ((COGTECH))

Summary

Granulation of the universe and approximation of concepts in a granulated universe are two related fundamental issues in the theory of rough sets. Many proposals dealing with the two issues have been made and studied extensively. We present a critical review of results from existing studies that are relevant to a decision-theoretical modeling of rough sets. Two granulation structures are studied: one is a partition induced by an equivalence relation, and the other is a covering induced by a reflexive relation. With respect to the two granulated views of the universe, element oriented and granule oriented definitions and interpretations of lower and upper approximation operators are examined. The structures of the families of fixed points of approximation operators are investigated. We start with the notions of rough membership functions and graded set inclusion defined by conditional probability. This enables us to examine different granulation structures and approximations induced in a decision-theoretical setting. By reviewing and combining results from existing studies, we attempt to establish a solid foundation for rough sets and to provide a systematic way of determining the parameters required in defining approximation operators.

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Author information

Authors and Affiliations

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

    Yiyu Yao

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  1. Yiyu Yao
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Editors and Affiliations

  1. Indian Statistical Institute, Machine Intelligence Unit, 203 Barrackpore Trunk Road, Calcutta, 700 035, India

    Sankar K. Pal

  2. Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, Olsztyn, Poland

    Lech Polkowski

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

    Andrzej Skowron

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© 2004 Springer-Verlag Berlin Heidelberg

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Yao, Y. (2004). Information Granulation and Approximation in a Decision-Theoretical Model of Rough Sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds) Rough-Neural Computing. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18859-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-18859-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62328-8

  • Online ISBN: 978-3-642-18859-6

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