Local and Global Measurements of MGRS Rules

Since the multigranulation rough sets (MGRS) can be considered as the compositions of multi– independent Pawlak’s rough sets, the multigranulation rough set rules (MGRS rules) are then the compositions of decision rules, which are supported by multi–independent Pawlak’s rough sets. To measure MGRS rules, both the local and global views are employed in this paper. In local view, the support, certainty and coverage factors are proposed to measure MGRS rules, which are support by an object; while in global view, these three factors are proposed to measure MGRS rules, which are coexisting in a decision system. The necessary conditions for these factors to achieve maximal and minimal values are also addressed. Some numerical examples are employed to substantiate the conceptual arguments.