Fully Interpretable Gaussian Centralized TSK Fuzzy Classifier From Probabilistic Perspective: Concepts, Output-Stability-Based Learning, and Ensemble

While a Gaussian centralized TSK fuzzy system seeks full interpretability, its existing training method may become infeasible. In this study, we investigate the system's promising modeling performance and full interpretability by revisiting it from a probabilistic perspective. This approach allows us to precisely identify its output as the mathematical expectation and to derive its output variance as a novel Output Stability (OS) metric, which can be used to measure output stability and generate a calibrated probability output for model calibration. Subsequently, a novel OS-based training method for a fully interpretable Gaussian centralized TSK fuzzy classifier is developed to enhance its modeling performance. In addition, another potential value of OS as its new application is also exploited in linear aggregation learning of such fully interpretable fuzzy subsystems. Experimental results on 14 benchmark binary datasets demonstrate the effectiveness of both the OS-based training method and the OS-based linear aggregation learning in terms of average testing classification performance, interpretability, and training time.