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Algebra and Topology for Dominance-Based Rough Set Approach

  • Salvatore Greco
  • Benedetto Matarazzo
  • Roman Słowiński
Chapter
Part of the Studies in Computational Intelligence book series (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.

Keywords

Decision Attribute Decision Class Priestley Space Interior Operator Indiscernibility Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Salvatore Greco
    • 1
  • Benedetto Matarazzo
    • 1
  • Roman Słowiński
    • 2
    • 3
  1. 1.Faculty of EconomicsUniversity of CataniaCataniaItaly
  2. 2.Institute of Computing SciencePoznań University of TechnologyPoznań
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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