A dynamic framework for updating neighborhood multigranulation approximations with the variation of objects

Abstract

Rough approximations play a significant role in rule extraction and decision making. However, re-scanning the entire data set to update the approximations is time-consuming due to the dynamic characteristics of objects in a neighborhood multigranulation space. In order to reduce the computational time, the neighborhood multigranulation approximations need to be updated in an incremental manner based on previously saved knowledge. Therefore, in this study, we establish a dynamic framework for maintaining the positive, boundary, and negative regions in neighborhood multigranulation spaces when adding or deleting objects from the matrix perspective. First, we explore the incremental mechanisms for updating relevant matrices when adding or deleting multiple objects. Based on the proposed mechanisms, we design the corresponding dynamic algorithms to incrementally update the positive, boundary, and negative regions. Finally, we conduct empirical experiments on benchmark UCI data sets to assess the feasibility and efficiency of our updating algorithms, which demonstrate their promising performance.