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Rough Sets Determined by Quasiorders

Jouni Järvinen, Sándor Radeleczki, Laura Veres, Rough Sets Determined by Quasiorders . arXiv:0810.0633, 2008.

Abstract:

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of $R \\cap R^-1$ does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.

BibTeX entry:

@TECHREPORT{tJaRaVe08a,
  title = {Rough Sets Determined by Quasiorders },
  author = {Järvinen, Jouni and Radeleczki, Sándor and Veres, Laura},
  year = {2008},
}

Belongs to TUCS Research Unit(s): Algorithmics and Computational Intelligence Group (ACI)

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