Covering-based multi-granulation fuzzy rough sets

As a new and meaningful extension of the Pawlak rough set, multi-granulation rough sets (MGRSs) have attracted much attention and fruitful achievements have been reported in different aspects. By combining with fuzzy rough set, the paper introduces multi-granulation fuzzy rough sets in the covering approximation space, namely, covering-based multi-granulation fuzzy rough sets (CMFRS), which form the extension of fuzzy rough sets. We first investigate several important properties of lower and upper approximations of concepts in covering-based multi-granulation fuzzy rough sets and elaborate on the differences between the proposed models and the existing ones in literature. By employing the notions of reduct and exclusion of a covering, the paper studies the necessary and sufficient conditions for two CMFRS to generate identical lower and upper approximations of a target concept in the given covering approximation space. Finally, the relationships between the new models are explored in the paper.