The comparative study of covering rough sets and multi-granulation rough sets

The covering rough set (CRS) theory and the multi-granulation rough set (MGRS) theory are both the important generalizations of Pawlak rough set theory. Up to now, substantial contributions have been made to the development of CRS and MGRS. In this paper, in order to shed some light on the comparison and combination of CRS theory and MGRS theory, we investigate the relationship between CRS and MGRS based on different aspects. We firstly put forward an effective approach to describe the covering rough sets by means of the multi-granulation rough sets. Then, we, respectively, study the differences and relations of lower and upper operators, reduction, operation properties and algebraic properties between CRS and MGRS.