Matrix-based fast granularity reduction algorithm of multi-granulation rough set

Yi Xu, Min Wang, Shanzhong Hu

Abstract: In order to overcome the limitation of low efficiency of existing granularity reduction algorithms in multi-granulation rough sets, based on matrix method, a fast granularity reduction algorithm is proposed and the time complexity is \(O({|U |}^{2} \cdot |A |+ |U|\cdot {|A |}^{2})\). First, the definitions of positive region matrix and granularity column matrix of multi-granulation space are proposed. Second, through the quantity product of these two matrices, the definition of positive region column matrix is presented. Based on the positive region column matrix, cut matrix and matrix norm are defined, respectively. Third, the matrix-based calculation methods of multi-granulation approximation quality and granularity significance are proposed. Finally, a heuristic rule is designed according to the granularity significance, and a matrix-based fast granularity reduction algorithm is proposed. Experimental results demonstrate the effectiveness of the proposed methods.