English

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 RR 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 RR 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

R2 v1 2026-06-21T11:27:05.673Z