Fuzzy rule-based network: a fuzzy logic-based interpretable and modular machine learning model

Abstract This paper introduces the Fuzzy Rule-Based Network (FRBN or FN), a novel machine learning architecture designed to bridge the gap between high-performance modeling and human-understandable decision-making. By combining the layered, hierarchical structure of artificial neural networks (NN) with the logical transparency of fuzzy systems, the FN operates as an interpretable “gray-box” model. Unlike traditional “black-box” neural networks that obscure their internal logic, the FN explicitly encodes its learned knowledge using fuzzy “if-then” rules at every layer, providing structural modularity and insight into how decisions are made. To optimize both FN and NN models, various strategies were comprehensively evaluated, including first-order gradient methods such as Adam, the quasi-second-order Levenberg–Marquardt algorithm, the gradient-free Bacterial Evolutionary Algorithm (BEA), and a hybrid Bacterial Memetic Algorithm (BMA) implemented for both neural and fuzzy network models. The predictive accuracy, structural modularity, and interpretability of the proposed FN model were assessed on several synthetic regression benchmarks, including the sinc function (where the FN model achieved a best-fold validation MSE of $$6.2 \times 10^{-8}$$ ), a multidimensional trigonometric dataset and validated on an industrial Micro-Electromechanical Systems (MEMS) sensor dataset. These experimental results demonstrate that the FN model provides a solution competitive with the NN model in terms of accuracy and training efficiency. The experiments demonstrate how the structural modularity of the FN model enables the reduction of parameters through the post-hoc extraction of localized sub-models. These specific fuzzy rule-sets maintain the exact predictive accuracy of the full model within their designated sub-intervals. The study further illustrates how the significance score identifies which specific rules govern particular subdomains, while the minimum antecedent coverage ratio evaluates the spatial scope of rules to distinguish between global and local influences. Additionally, the model’s interpretability is validated on the MEMS dataset, where linguistic interpretations are associated with the fuzzy rules. The FN can be initialized using domain knowledge, which stabilizes and accelerates training convergence. Finally, the trained rules can be translated back into human-understandable if-then statements, representing a step towards transparent decision-making.