The relationship between coverings and tolerance relations Online publication date: Sat, 20-Nov-2010
by Xiaoli Song, Guilong Liu, Jie Liu
International Journal of Granular Computing, Rough Sets and Intelligent Systems (IJGCRSIS), Vol. 1, No. 4, 2010
Abstract: A tolerance relation is a relation that is reflexive and symmetric. The concept of a covering is an extension of that of a partition. Tolerance relations and covering rough sets provide a general tool for studying indiscernibility phenomena. This paper studies the relationship between tolerance relations and coverings. We show that with any covering, we can associate a tolerance relation and vice versa, for which the upper approximations are invariant under the procedure. Finally, we give an axiomatic characterisation of the second type of covering upper approximations.
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