The relationship between coverings and tolerance relations
Xiaoli Song, Guilong Liu, Jie Liu · International Journal of Granular Computing Rough Sets and Intelligent Systems · 2010
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.