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Rough Sets Determined by Quasiorders

Jouni Järvinen, Sándor Radeleczki, Laura Veres, Rough Sets Determined by Quasiorders. Order 26, 337-355, 2009.

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. We show that on this lattice can be defined three different
kinds of complementation operations, and we describe its completely join-
irreducible and its completely meet-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 (Bull Pol Acad Sci, Math, 36:495-
512, 1988) and M. Gehrke and E. Walker (Bull Pol Acad Sci, Math, 40:235-
245, 1992 in case R is an equivalence.

DOI: 10.1007/s11083-009-9130-z

BibTeX entry:

@ARTICLE{jJaRaVe09a,
  title = {Rough Sets Determined by Quasiorders},
  author = {Järvinen, Jouni and Radeleczki, Sándor and Veres, Laura},
  journal = {Order },
  volume = {26},
  pages = {337-355},
  year = {2009},
}

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

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