Fuzziness-Based Three-Way Decision With Neighborhood Rough Sets Under the Framework of Shadowed Sets

Jie Yang, Xiaoqi Wang, Guoyin Wang, Qinghua Zhang, Nenggan Zheng, Di Wu

Abstract: Currently, three-way decision with neighborhood rough sets (3WDNRS) is widely used in many fields. The core of 3WDNRS is to calculate threshold pairs to divide a neighborhood space into three pairwise disjoint regions. The majority of research on 3WDNRS mainly aims to calculate thresholds with the given risk parameters to minimize the misclassification cost. However, in practical applications, risk parameters are often subjectively determined based on expert experience. This makes it challenging to accurately obtain the thresholds in 3WDNRS. To solve this problem, fuzziness is introduced into 3WDNRS to provide a new perspective on 3WD theory. First, a shadowed set framework is constructed, named three-way approximations based on shadowed sets (3WA-SS). Based on 3WA-SS, a data-driven adapted neighborhood (DAN) is constructed. Then, an improved fuzziness-based 3WDNRS (F $^{\prime }$ -3WDNRS) is further proposed and optimized by minimizing uncertainty change to obtain a more reasonable threshold pair based on DAN. Finally, extensive experiments are conducted on our proposed model, and the results show that F $^{\prime }$ -3WDNRS is effective and reliable for making decisions.