An attribute reduction algorithm using relative decision mutual information in fuzzy neighborhood decision system

The fuzzy neighborhood rough set integrates the strengths of fuzzy rough set and neighborhood rough set, serving as a pivotal extension of the rough set theory in attribute reduction. However, this model's widespread application is hindered by its sensitivity to data distribution and limited efficacy in assessing classification uncertainty for datasets with substantial density variations. To mitigate these challenges, this paper introduces an attribute reduction algorithm based on fuzzy neighborhood relative decision mutual information. Firstly, the classification uncertainty of samples is initially defined in terms of relative distance. Simultaneously, the similarity relationship of fuzzy neighborhoods is reformulated, thereby reducing the risk of sample misclassification through integration with variable-precision fuzzy neighborhood rough approximation. Secondly, the notion of representative sample is introduced, leading to a redefinition of fuzzy membership. Thirdly, fuzzy neighborhood relative mutual information from the information view is constructed and combined with fuzzy neighborhood relative dependency from the algebraic view to propose fuzzy neighborhood relative decision mutual information. Finally, an attribute reduction algorithm is devised based on fuzzy neighborhood relative decision mutual information. This algorithm evaluates the significance of attributes by integrating both informational and algebraic perspectives. Comparative tests on 12 public datasets are conducted to assess existing attribute approximation algorithms. The experimental results show that the proposed algorithm achieved an average classification accuracy of 91.28%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} with the KNN classifier and 89.86%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} with the CART classifier. In both classifiers, the algorithm produced an average reduced subset size of 8.54. While significantly reducing feature redundancy, the algorithm consistently maintains a high level of classification accuracy.