On the coverings by tolerance classes

  • Authors:

  • W. Bartol;J. Miró;K. Pióro;F. Rosselló

  • Affiliations:

  • Institute of Mathematics, University of Warsaw, 02-097 Warsaw, Poland;Department of Mathematics and Computer Science, Research Institute of Health Science (IUNICS), University of the Balearic Islands, Crta. Valldemossa, Km. 7'5 E-07122 Palma de Mallorca, Spain;Institute of Mathematics, University of Warsaw, 02-097 Warsaw, Poland;Department of Mathematics and Computer Science, Research Institute of Health Science (IUNICS), University of the Balearic Islands, Crta. Valldemossa, Km. 7'5 E-07122 Palma de Mallorca, Spain

  • Venue:
  • Information Sciences—Informatics and Computer Science: An International Journal
  • Year:
  • 2004

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Abstract

A tolerance is a reflexive and symmetric, but not necessarily transitive, binary relation. Contrary to what happens with equivalence relations, when dealing with tolerances one must distinguish between blocks (maximal subsets where the tolerance is a total relation) and classes (the class of an element is the set of those elements tolerable with it). Both blocks and classes of a tolerance on a set define coverings of this set, but not every covering of a set is defined in this way. The characterization of those coverings that are families of blocks of some tolerance has been known for more than a decade now. In this paper we give a characterization of those coverings of a finite set that are families of classes of some tolerance.