ar X iv : 0 81 0 . 06 33 v 2 [ m at h . R A ] 1 6 Ju n 20 09 ROUGH SETS DETERMINED BY QUASIORDERS
نویسنده
چکیده
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 elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomyka la and J. A. Pomyka la (1988) and M. Gehrke and E. Walker (1992) in case R is an equivalence.
منابع مشابه
ar X iv : 0 81 0 . 06 33 v 1 [ m at h . R A ] 3 O ct 2 00 8 ROUGH SETS DETERMINED BY QUASIORDERS
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∩R does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we d...
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تاریخ انتشار 2009