ROUGH SETS DETERMINED BY QUASIORDERS
Jouni Järvinen, Sändor Radeleczki, Laura Veres · 2012
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 elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomyka̷la and J. A. Pomyka̷la (1988) and M. Gehrke and E. Walker (1992) in case R is an equivalence.