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Rough Sets Determined by Quasiorders

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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. Pomykała and J. A. Pomykała (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.

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Authors and Affiliations

  1. Department of Information Technology, University of Turku, 20014, Turku, Finland

    Jouni Järvinen

  2. Institute of Mathematics, University of Miskolc, 3515, Miskolc-Egyetemváros, Hungary

    Sándor Radeleczki & Laura Veres

Authors
  1. Jouni Järvinen
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  2. Sándor Radeleczki
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  3. Laura Veres
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Corresponding author

Correspondence to Jouni Järvinen.

Additional information

The partial support by Hungarian National Research Found (Grant No. T049433/05 and T046913/04) is acknowledged by the second author.

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Järvinen, J., Radeleczki, S. & Veres, L. Rough Sets Determined by Quasiorders. Order 26, 337–355 (2009). https://doi.org/10.1007/s11083-009-9130-z

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