Attribute Reduction Based on Fuzzy Distinguishable Pair Metric Considering Redundancy Upper and Lower Bounds

Attribute reduction, also called feature selection, serves as a widely adopted approach to reduce data processing complexity by eliminating irrelevant and redundant attributes. It plays a crucial role in addressing the challenges associated with high-dimensional data, optimizing computational resources, and enhancing learning performance. A well-designed attribute reduction method can effectively streamline data analysis processes and improve the overall efficiency and effectiveness of machine learning algorithms. To some extent, the quantity of information contained in an information system can be regarded as the number of distinguishable sample pairs it contains. In this article, the fuzzy distinguishable pair metric is proposed to measure the uncertainty. This metric measures uncertainty by comprehensively considering the number of fuzzy distinguishable pairs and the cardinality of fuzzy similarity relation. Correspondingly, variants of the fuzzy distinguishable pair metric such as joint distinguishable pair metric, conditional distinguishable pair metric, and mutual distinguishable pair metric are constructed. Moreover, the concepts of selected features redundancy upper bound and selected features redundancy lower bound are proposed. These two terms can be flexibly applied to the importance measure to alleviate the problem of over- or under-consideration redundancy. Considering the upper and lower bounds of the selected feature redundancy respectively, two new importance measures are proposed. Based on the previously proposed theory, two attribute reduction algorithms are designed. Finally, comparing the proposed two methods with six effective attribute reduction methods on eighteen datasets with four classifiers, our method achieves good results.