Approaches to attribute reduction of metric-fuzzy decision systems based on information theory

Abstract

Fuzzy rough sets and information theory are both effective tools for processing large-scale data. This study combines the advantages of both to establish the attribute reduction theory and the method of metric fuzzy information systems based on information theory. First, it defines the concepts of metric fuzzy rough entropy, fuzzy joint rough entropy and fuzzy rough mutual information, explores their properties and relationships and constructs a method for evaluating attribute importance. Secondly, based on this theoretical foundation, two efficient attribute reduction algorithms are designed: the first algorithm doesn't rely on decision attributes, and its advantage is that it can effectively improve the computational efficiency; the second algorithm combines decision attributes, and its advantage is that it can optimize the reduction effect. Both algorithms use the strategies of forward selection and backward elimination to eliminate redundant attributes. Finally, this paper compares these two reduction algorithms with five commonly used reduction algorithms on 20 datasets and uses the average classification accuracy of 14 classifiers to evaluate the reduction effects of these algorithms. Experimental results show that the two algorithms proposed in this paper perform well in classification tasks, with their average accuracy ranking among the highest compared to other algorithms, thus verifying the efficiency and advantages of the reduction algorithms of metric fuzzy information systems in large-scale data processing.