Generalized weighted neighborhood rough sets

Abstract

Neighborhood rough sets have been effectively applied to handling numerical data. To more accurately reflect the influence of each condition attribute on the decision attributes, attribute-weighted neighborhood rough sets have been introduced to assign weights to condition attributes when constructing information granules. Additionally, another approach concentrates on weighting objects within granules, aiming to address noisy and unevenly distributed data. However, these approaches only allow the application of weights to either attributes or objects, but not both. Therefore, we propose a novel generalized weighted neighborhood rough set model (GWNRSs), wherein information granules are constructed through a comprehensive evaluation of attribute and object weights. While inheriting the strengths of two previously mentioned approaches, our model also effectively addresses objects in the boundary region, often neglected in traditional models. Theoretically, we present fundamental concepts of GWNRSs and state its essential properties. These properties emphasize that several existing neighborhood rough set models are particular cases of GWNRSs. Next, we develop a robust attribute reduction algorithm based on GWNRSs. Experimentally, we implement the proposed algorithm on various benchmark datasets and compare its performance with other state-of-the-art algorithms. The results in terms of classification accuracy and reduct size demonstrate the superiority of GWNRSs through statistical evaluations.