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Algebra and Topology for Dominance-Based Rough Set Approach

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Advances in Intelligent Information Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 265))

Abstract

Dominance-based rough sets generalize classical indiscernibility based rough sets by handling ordered value sets of attributes and monotonic relationships between values of condition and decision attributes. Dominance based rough sets permit, in particular, a natural hybridization of fuzziness and roughness, which are complementary concepts of vagueness. In this article, we characterize the Dominance-based Rough Set Approach (DRSA) from the point of view of its mathematical foundations, taking into account algebraic structures and topological properties. We present algebraic representations of DRSA in terms of generalizations of several algebras already used to represent the classical rough set approach, namely: bipolar de Morgan Brouwer-Zadeh distributive lattice, bipolar Nelson algebra, bipolar Heyting algebra, bipolar double Stone algebra, bipolar three-valued Łukasiewicz algebra, bipolar Wajsberg algebra.We also present an algebraic model for ordinal classification. With respect to topological properties, using the concept of a bitopological space, we extend on DRSA the results obtained for classical rough sets.

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Author information

Authors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo

  2. Institute of Computing Science, Poznań University of Technology, 60-965, Poznań

    Roman Słowiński

  3. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

Authors
  1. Salvatore Greco
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  2. Benedetto Matarazzo
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  3. Roman Słowiński
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of North Carolina, N.C. 28223, Charlotte, USA

    Zbigniew W. Ras

  2. Department of Electronics, Computer & Information Technology, NC A &T State University, NC 27411, Greensboro, USA

    Li-Shiang Tsay

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Greco, S., Matarazzo, B., Słowiński, R. (2010). Algebra and Topology for Dominance-Based Rough Set Approach. In: Ras, Z.W., Tsay, LS. (eds) Advances in Intelligent Information Systems. Studies in Computational Intelligence, vol 265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05183-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-05183-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05182-1

  • Online ISBN: 978-3-642-05183-8

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