Feature selections integrating algebraic and information perspectives in weighted incomplete neighborhood rough sets

Abstract

In data-driven scientific research and practical applications, data incompleteness and uncertainty are widespread issues that have become critical bottlenecks, restricting the accuracy of data analysis and the reliability of decision-making. Addressing the limitations of existing incomplete rough set models, which predominantly focus on uncertainty measurement adjustment while overlooking feature weighting and neighborhood relation construction, this paper proposes feature selection methods based on a weighted incomplete neighborhood rough set framework, integrating algebraic and information perspectives. Firstly, a weighted tolerance neighborhood relation is introduced to better quantify uncertainty, enhancing adaptability in classification and feature selection tasks. Secondly, from the algebraic perspective, three weighted measures are developed: weighted approximation accuracy, weighted information granularity, and weighted approximation precision based on information granularity. These measures are combined with information-theoretic metrics such as mutual information, complementary mutual information, and self-information to form nine fusion measures. Finally, a unified feature selection algorithmic framework is designed to comprehensively evaluate feature importance. Experimental results demonstrate that the proposed methods significantly improve classification accuracy across 12 datasets. Notably, under a 10% incompleteness rate, the GASI-FS, GMI-FS, and AMI-FS algorithms achieve classification accuracies of 87.31%, 85.87%, and 86.79% on KNN, CART, and SVM classifiers, respectively, outperforming other methods. These findings provide a robust theoretical foundation and practical tools for analyzing incomplete data in complex scenarios.