Adaptive Relative Fuzzy Rough Learning for Classification

Fuzzy rough set theory offers a valuable approach for addressing data uncertainty; however, existing fuzzy rough sets often failed to capture data distribution in practical applications due to their limited adaptive learning capabilities. This article aims to enhance the data fitting ability of fuzzy rough set theory by incorporating an adaptive learning mechanism. Consequently, this study introduces a relative fuzzy rough set model with adaptive learning (ALRFRS), where the adaptive learning mechanism considers not only feature weights but also class variances. To describe the similarity between samples in data regions with significant differences in class density, this study introduces the concepts of relative distance and relative fuzzy similarity relation. Subsequently, the study defines relative fuzzy rough approximation operators for each feature and combines them based on varying feature weights to establish a relative fuzzy rough set model. In addition, the study conducts an analysis of some fundamental properties of the model. To enable adaptive fuzzy rough learning, the study formulates an objective function that incorporates feature weights and class variances and provides the corresponding optimization learning algorithm. Experimental results demonstrate that the adaptive learning mechanism can enhance the classification accuracy of relative fuzzy rough models, surpassing the performance of most existing excellent algorithms.