%0 Journal Article
%T Rough Sets Determined by Quasiorders
%A Jouni J£¿rvinen
%A S¨¢ndor Radeleczki
%A Laura Veres
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s11083-009-9130-z
%X 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.
%U http://arxiv.org/abs/0810.0633v2