Topological approach to multigranulation rough sets

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to characterize the uncertainty of the multigranulation topological rough space. Finally, based on the invariance of interior and closure operators of a target concept, a granulation selection algorithm is introduced to deal with the granularity selection issue in the multigranulation rough data analysis.