Document (#36843)

Author

Bartol, W.
Pióro, K.
Rosselló, F.

Title

On the coverings by tolerance classes

Source

Information sciences: informatics and computer science. 166(2004) nos.1-4, S.193-211

Year

2003

Abstract

A tolerance is a reflexive and symmetric, but not necessarily transitive, binary relation. Contrary 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.

Content

Preprint unter: http://bioinfo.uib.es/recercagrup/tolerances.pdf.

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