Rough Sets Determined by Quasiorders

Details Rough Sets Determined by Quasiorders Rough Sets Determined by Quasiorders

2008-10-03

arxiv.org/abs/0810.0633v2

Mathematics

Rings and Algebras

18 pages, major revision

Scientific paper

10.1007/s11083-009-9130-z

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. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.

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