Fusion and comparison of multi-granulation rough sets

Multi-granulation rough sets are extended rough set models, which are based on a family of equivalence relations on universe of discourse. By applying join or intersection operations of binary relations, in this paper, two binary relations are defined in a multi-granulation approximation space, consequently two types of rough sets are introduced. Subsequently, in the views of approximation space fusion and approximation operator fusion, two types of rough sets in a multi-granulation approximation space are analyzed. Finally, comparison among the multi-granulation rough sets are made, and conditions for these approximation operators to be equivalent are obtained.