Rough Sets Determined by Quasiorders
Rings and Algebras
2014-03-26 v2
Abstract
In this paper, the ordered set of rough sets determined by a quasiorder relation 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 is an equivalence.
Keywords
Cite
@article{arxiv.0810.0633,
title = {Rough Sets Determined by Quasiorders},
author = {Jouni Järvinen and Sándor Radeleczki and Laura Veres},
journal= {arXiv preprint arXiv:0810.0633},
year = {2014}
}
Comments
18 pages, major revision