Rough Sets Determined by Quasiorders |
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| Authors: | Jouni Järvinen Sándor Radeleczki Laura Veres |
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| Institution: | 1.Department of Information Technology,University of Turku,Turku,Finland;2.Institute of Mathematics,University of Miskolc,Miskolc-Egyetemváros,Hungary |
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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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