Attribute Reduction and Optimal Scale Combination Selection Based on Variable Precision Entropy in Multi-scale Decision Systems
GUO Ruili1,2, ZHANG Qinghua2,3, YANG Ying1,2, CHENG Yunlong4, ZHONG Hang1,2
1. School of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065; 2. Key Laboratory of Cyberspace Big Data Intelligent Security of Ministry of Education, Chongqing University of Posts and Tele-communications, Chongqing 400065; 3. Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications, Chongqing 400065; 4. School of Mathematics and Statistics, Chongqing University of Posts and Telecommunications, Chongqing 400065
Abstract：Most existing multi-scale decision systems are built on Pawlak rough sets and their tolerance to noisy data is limited. Although variable precision is introduced to enhance the adaptability in uncertain environments, current methods typically perform scale selection before attribute reduction. Thus, it is difficult to fully leverage attribute reduction in reducing computational complexity. Though information entropy is applied to multi-scale data analysis, its capability to characterize uncertainty relationships within variable precision multi-scale rough set models still needs to be improved. To address these issues, an attribute reduction and optimal scale combination selection method based on variable precision complementary conditional entropy is proposed. First, a monotonic variable precision complementary conditional entropy is presented to characterize the uncertainty relationships between condition attributes and decision attributes under arbitrary scale combinations. Based on this entropy, a consistency-based attribute reduction method is developed. Redundant attributes are effectively eliminated while decision information is preserved. Second, an optimal attribute reduction method based on classification performance is proposed to enhance the effectiveness of the reduction results in classification tasks. On this basis, an optimal scale combination selection algorithm is further designed by incorporating the obtained reduced attribute set to effectively reduce the scale search space. The experiments on UCI datasets demonstrate the effectiveness of the proposed method in terms of classification performance and robustness.
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2026, Vol. 39 
