@MISC{INTERVA1.MIZ,
  AUTHOR = {Grabowski, Adam and Jastrz\c{e}bska, Magdalena},
  TITLE = {On the Lattice of Intervals and Rough Sets},
  SECTION1 = {Interval Sets},
  SECTION2 = {Families of Subsets},
  SECTION3 = {Counterexamples},
  SECTION4 = {Lattice of Interval Sets},
  SECTION5 = {Lattice of Rough Sets},
  DAY = {10},
  MONTH = {October},
  YEAR = {2009},
  ADDRESS1 = {Institute of Mathematics\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok\\Poland},
  ADDRESS2 = {Institute of Mathematics\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok\\Poland},
  SUMMARY = {Rough sets, developed by Pawlak, are important tool to
  describe situation of incomplete or partially unknown information.
  On of the algebraic models is the pair of the upper and the lower
  approximation. Although usually the tolerance or the equivalence
  relation is taken into account when considering a rough set,
  we concentrate here rather at the model with the pair of two definable
  sets. Hence we are close to the notion of an interval set.
  In this article, the lattices of rough sets and intervals are formalized.
  This paper, being essentially the continuation of \cite{ROUGHS_1.ABS},
  is also a step towards the formalization of the algebraic theory
  of rough sets, as in \cite{Mousavi:2001} or \cite{Yao:1993}.}}

@ARTICLE{Mousavi:2001,
 AUTHOR={Mousavi, Amin and Jabedar-Maralani, Parviz},
 TITLE={Relative Sets and Rough Sets},
 JOURNAL={Int. J. Appl. Math. Comput. Sci.},
 VOLUME = 11,
 NUMBER = 3,
 PAGES = {637--653},
 YEAR=2001}

@ARTICLE{Yao:1993,
 AUTHOR={Yao, Y.Y.},
 TITLE={Interval-set Algebra for Qualitative Knowledge Representation},
 JOURNAL={Proc. 5-th Int. Conf. Computing and Information},
 PUBLISHER = {IEEE Computer Society Press},
 PAGES = {370--375},
 YEAR=1993}

