Parameterized maximum-entropy-based three-way approximate attribute reduction

Abstract

Three-way decision theory has emerged as an effective method for attribute reduction when dealing with vague, uncertain, or imprecise data. However, most existing attribute reduction measures in the three-way decision are non-monotonic and too strict, limiting the quality of attribute reduction. In this study, a monotonic measure called parameterized maximum entropy (PME) is proposed for approximate attribute reduction. Specifically, considering that the classification ability under uncertainty is reflected by both the decision and the degree of confidence, a novel PME measure that attaches different levels of importance to the decision with the highest probability and other decisions is provided, and its monotonicity is theoretically proven. Furthermore, the idea of trisection in the three-way decision is introduced into the process of attribute reduction, and a heuristic algorithm based on the proposed measure is developed to generate an optimal three-way approximate reduct, which greatly improves the efficiency of attribute reduction. Several experiments conducted on UCI datasets show that the proposed method achieves a favorable performance with much fewer attributes in comparison with other representative methods.