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The Ordered Set of Rough Sets

Jouni Järvinen, The Ordered Set of Rough Sets. In: Roman Slowinski Jan Komorowski et al. (eds.) Shusaku Tsumoto (Ed.), Proceedings of the Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC 2004), Lecture Notes in Artificial Intelligence 3066, 49-58, 2004.

Abstract:

We study the ordered set of rough sets determined by relations which
are not necessarily reflexive, symmetric, or transitive.We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the ordered sets of rough sets that are not necessarily lattices we present some possible canonical completions.

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BibTeX entry:

@INPROCEEDINGS{inpJarvinen04a,
  title = {The Ordered Set of Rough Sets},
  booktitle = {Proceedings of the Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC 2004)},
  author = {Järvinen, Jouni},
  volume = {3066},
  series = {Lecture Notes in Artificial Intelligence},
  editor = {Shusaku Tsumoto, Roman Slowinski Jan Komorowski et al. (eds.)},
  pages = {49-58},
  year = {2004},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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