Matrix-based approaches for dynamic updating approximations in multigranulation rough sets

Multigranulation rough set, which is constructed by a family of equivalence relations has attracted much attention, because it offers a theoretical framework for the problem solving in the view of multigranulation. However, the granular structure in the information systems often dynamically evolves over time. How to dynamically obtain the potential useful knowledge for decision making is of great significance in the context of multigranulation. Motivated by this requirement, in this paper, we present the definitions of equivalence relation matrix, diagonal matrix and cut matrix for a single granular structure in multigranulation rough set, and propose a matrix representation of multigranulation approximations in optimistic and pessimistic multigranulation rough set. Then, corresponding matrix-based dynamic approaches for updating approximations are proposed in multigranulation rough set when a single granular structure evolves over time. The experimental evaluations show the effectiveness of the proposed matrix-based dynamic updating algorithms compared with the matrix-based static algorithm.