Title: The relationship between coverings and tolerance relations

Authors: Xiaoli Song, Guilong Liu, Jie Liu

Addresses: School of Information Science, Beijing Language and Culture University, Beijing 100083, China. ' School of Information Science, Beijing Language and Culture University, Beijing 100083, China. ' School of Information Science, Beijing Language and Culture University, Beijing 100083, China

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.

Keywords: tolerance relations; granular computing; covering rough sets; axiom; upper approximation; partition.

DOI: 10.1504/IJGCRSIS.2010.036977

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2010 Vol.1 No.4, pp.343 - 354

Available online: 20 Nov 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article