Matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation

Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation.