Incremental updating knowledge in neighborhood multigranulation rough sets under dynamic granular structures.

Neighborhood Multigranulation Rough Sets (NMGRS), constructed by a family of neighborhood relations, can effectively obtain required knowledge from Neighborhood Information Systems (NIS). In various practical situations, NIS may alter dynamically with time. Incremental learning is an alternative manner for maintaining knowledge by utilizing previous computational results under dynamic data contexts. In dynamic NIS with numerical data, potential useful knowledge, e.g., the positive, boundary and negative regions in NMGRS, needs to be updated for various applications. To address this issue, we present matrix-based incremental approaches to update knowledge in NMGRS with the addition or deletion of granular structures. First, a matrix-based representation of neighborhood multigranulation rough approximations is developed. Then, the matrix-based dynamic strategies are proposed to update the positive, boundary, and negative regions in the optimistic and pessimistic NMGRS under the variation of a granular structure. In accordance with the proposed updating strategies, the matrix-based dynamic algorithms are explored for maintaining the positive, boundary and negative regions while adding or deleting granular structures. Finally, comparative experiments are conducted to show that the matrix-based dynamic algorithms are feasible and effective.