Int. J. of Granular Computing, Rough Sets and Intelligent Systems   »   2010 Vol.1, No.4

 

 

Title: The relationship between coverings and tolerance relations

 

Author: 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

 

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

 

Available online: 20 Nov 2010

 

 

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