Vector-based approaches for computing approximations in multigranulation rough set

Approximation computation is a significant issue when the rough set model is applied. However, few authors focus on how to calculate approximations of multigranulation rough set (MGRS). Herein, the authors clarify a fact that only a part of elements in the universe need to be judged whether they belong to approximations of MGRS. If X is a target concept which is approximated by approximations in MGRS, then the element whose equivalence class does not intersect with X is of no need to be judged. Based on the fact, the authors clarify that they proposed a vector-based algorithm to compute approximations in MGRS. Time complexity of the proposed algorithm is O(vertical bar X vertical bar vertical bar U vertical bar ).