Generalized Gradient of Positive Adaptive-Compensation-Based for Fuzzy Hierarchical Classification

Abstract

Hierarchical Takagi–Sugeno–Kang (TSK) fuzzy classifiers combine nonlinear modeling with rule-based decision structures for complex classification tasks. However, prediction errors may propagate through successive layers, and the contributions of different layers require careful consideration when combining their outputs. These limitations motivate a learning strategy that incorporates inter-layer information and adjusts layer contributions. This study proposes a hierarchical TSK fuzzy classifier with adaptive error compensation (DAE-TSK-FC). The adaptive error compensation mechanism incorporates prediction differences between successive layers into subsequent layer inputs while retaining supervision from true labels. A soft relaxation-based output ensemble strategy combines supervised base coefficients with output-dependent adjustments to determine the weights assigned to different layers. Experiments compare DAE-TSK-FC with five benchmark classifiers on six UCI datasets and three real-world rice wine fermentation datasets. The proposed method achieves the highest mean testing accuracies on Iris, FJ-BJ-PCI, and FJ-BQ-PCI, reaching 98.38%, 96.25%, and 92.67%, respectively, and exhibits the smallest testing-accuracy standard deviations on Iris and FJ-BJ-PCI. Moreover, the proposed model preserves the interpretable structure of TSK fuzzy rules, allowing its predictions to be explained through the semantic meanings of fuzzy antecedents and the contributions of rule consequents.