Rough Sets Determined by Quasiorders

@article{Jrvinen2009RoughSD,
  title={Rough Sets Determined by Quasiorders},
  author={Jouni J{\"a}rvinen and S{\'a}ndor Radeleczki and Laura Veres},
  journal={Order},
  year={2009},
  volume={26},
  pages={337-355}
}
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, whenever the partially ordered set of the equivalence classes of R∩R−1 does not contain infinite ascending chains. 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… CONTINUE READING

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