Variable radius neighborhood rough sets and attribute reduction

Abstract

Neighborhood rough sets provide important insights into dealing with numerical data. Neighborhood radius, a key factor that affects data uncertainty, is uniformly given in most of the existing neighborhood rough sets. Although it is concise and convenient to construct a granular structure, the same radius is not appropriate for the unique circumstance of each element in the universe. Therefore, taking the different environment of each object and label distribution into consideration, in this paper, we propose two novel neighborhood rough set models, namely, variable radius neighborhood rough sets (VRNRs) and neighborhood rough sets based on α-covering (α-CNRSs). They customize the neighborhood radius for each object or local region of the universe by surrounding functions. Based on an investigation of the basic properties of VRNRs and α-CNRSs, we present two attribute reduction algorithms. Moreover, three comparative experiments are designed in terms of the running time, model stability, and classification accuracy. Theoretical analyses and experimental results show that the two new neighborhood rough set models have good robustness and validity in attribute reduction and classification performance.