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Abstract

We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the ordered sets of rough sets that are not necessarily lattices we present some possible canonical completions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jouni Järvinen
    • 1
  1. 1.Turku Centre for Computer Science (TUCS)TurkuFinland

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