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

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Abstract

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\(\%\) with the KNN classifier and 89.86\(\%\) 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.

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Data Availability

The low-dimensional datasets from the experiment were downloaded from http://archive.ics.uci.edu/ml/index.php and the high-dimensional datasets were downloaded from http://csse.szu.edu.cn/staff/zhuzx/.

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Acknowledgements

The paper is supported in part by the National Natural Science Foundation of China under Grant (61976082, 62002103).

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Conceptualization: Jiucheng Xu, Shan Zhang; Methodology: Shan Zhang; Writing - original draft preparation: Shan Zhang, Miaoxian Ma, Wulin Niu; Writing - review and editing: Shan Zhang, Jianghao Duan; Funding acquisition: Jiucheng Xu.

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Correspondence to Shan Zhang.

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Appendix A

Appendix A

In this section, we supplement certain figures from the main text. Figures 11 and 12 are radar charts plotted based on the classification accuracy of the algorithm across different datasets and classifiers. Tables 20, 21, 22, and 23 provide the rankings of the algorithm’s classification accuracy on various classifiers.

Fig. 11
figure 11

Radar charts of 7 algorithms on low-dimensional data

Fig. 12
figure 12

Radar charts of algorithms on high-dimensional data

Table 20 Ranking of 10 algorithms under KNN classifier
Table 21 Ranking of 6 algorithms under CART classifier
Table 22 Ranking of 7 algorithms under SVM classifier
Table 23 Ranking of 6 algorithms under NB classifier

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Xu, J., Zhang, S., Ma, M. et al. An attribute reduction algorithm using relative decision mutual information in fuzzy neighborhood decision system. Appl Intell 55, 217 (2025). https://doi.org/10.1007/s10489-024-06171-w

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