Relative Relation Matrix-Based Approaches for Updating Approximations in Multigranulation Rough Sets

Multigranulation rough set (MGRS) theory has attracted much attention. However, with the advent of big data era, the attribute values may often change dynamically, which leads to high computational complexity when handling large and complex data. How to effectively obtain useful knowledge from the dynamic information system becomes an important issue in MGRS. Motivated by this requirement, in this paper, we propose relative relation matrix approaches for computing approximations in MGRS and updating them dynamically. A simplified relative relation matrix is used to calculate approximations in MGRS, it is showed that the space and time complexities are no more than that of the original method. Furthermore, relative relation matrix-based approaches for updating approximations in MGRS while refining or coarsening attribute values are proposed. Several incremental algorithms for updating approximations in MGRS are designed. Finally, experiments are conducted to evaluate the efficiency and validity of the proposed methods.