Experimental results demonstrate that the Fuzzy Rule-Based Network model provides a solution competitive with the NN model in terms of accuracy and training efficiency, and the trained rules can be translated back into human-understandable if-then statements, representing a step towards transparent decision-making.
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.
In this study, we propose an incrementally expanding fuzzy neural module network (FNMN) designed to effectively handle both low- and high-dimensional problems without relying on dimensionality reduction techniques. The proposed framework adopts a modular and hierarchical architecture, in which univariate fuzzy neural modules (UFNMs) are incrementally selected and connected according to their representational capability, quantified by the coefficient of determination. The variable-specific univariate fuzzy rule architecture avoids exponential rule growth while preserving interpretability. A residual-driven hierarchy incrementally selects informative modules and progressively refines the model. A hybrid learning strategy combines efficient modulewise learning based on least squares error estimation with global fine-tuning via backpropagation (BP). Adam-based optimization is adopted to enhance convergence stability and reduce sensitivity to learning-rate settings. Extensive experiments on 28 publicly available benchmark datasets demonstrate the effectiveness of the proposed approach. The proposed method achieves an average performance improvement of 19% compared with a conventional fuzzy clustering-based model across diverse benchmarks. Statistical significance tests further confirm that the proposed model significantly outperforms recent neurofuzzy systems. Notably, competitive predictive performance is attained while model complexity is reduced by more than two orders of magnitude relative to deep learning approaches. These findings highlight the efficiency and scalability of the proposed framework.
Eun-Hu Kim, Hao Huang, Zheng Wang et al.· IEEE Transactions on Cyberne...· 0 citations
The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.
Haoran Pei, Zhao Su, Zetao Lin et al.· 0 citations
A new framework for Neuro-Symbolic Machine Learning (NS-ML) to enhance the adaptive decision intelligence of distributed smart systems is introduced. As smart environments become more complex, the transparency and reasoning of traditional black-box deep learning models in uncertain circumstances are unsatisfactory. Researchers address this deficit with a hybrid approach that combines neural networks (NNs), which excel at capturing perceptual patterns, and symbolic logic engines (SLEs), which excel at making decisions structured and explainable. The model uses both connectionist learning and formal knowledge representation to achieve high adaptability in a dynamic environment. The experimental study uses a well-defined set of 364 real-time sensor telemetry and operational event logs collected from an experimental smart grid infrastructure testbed. Researchers used Python to implement the framework and PyTorch for the neural parts, while the CLINGO engine handled the symbolic reasoning. The results show that our hybrid method is much more accurate in decision-making and logical consistency than using a neural network alone, especially when operational conditions vary. The framework offers a solid base for the development of self-optimising distributed systems, which must not only be capable of high-speed processing but also give assurance of decision-making logic, and is therefore suitable for modern industrial automation and smart city buildings.
Rajesh Mannam· FMDB Transactions on Sustain...· 0 citations
In this paper, we describe a new hybrid framework called FIS-CSP-OM that combines Fuzzy Inference Systems (FIS), Constraint Satisfaction Problems (CSP), and Optimization Modeling (OM) together for analysing and interpreting imbalanced datasets. The goal of the hybrid framework is to provide a means to integrate interpretable rule-based models (e.g., FIS) and numerical constraint-based reasoning (e.g., CSP and OM) in order to better represent imbalanced datasets and to understand the relationships among the variables used to create the model. Using triangular membership functions, we convert all of the numerical features into their corresponding linguistic variables, so that we can represent the dataset in a fuzzy manner. After the linguistic representation of the data is generated, we use the Apriori algorithm to perform association rule mining which enables us to create a set of high-confidence rules that can be used to describe and characterise the minority class. Finally, we can use the set of rules to develop a Linguistic CSP model that consists of symbolic variables that represent all of the linguistic features of the data and that have constraints that describe the relationships that were uncovered using the high-confidence rules. Following the transformation of the linguistic model into a Numerical CSP by identifying fuzzy modalities with continuous intervals, a tractable question will be derived from Constraint Solvers. Validation of the methodology is performed on the imbalanced dataset where the focus is on the minority class, ‘young.’ Experimental results demonstrate that there is a high degree of confidence in the extracted rules and a great deal of structural coherence between them, yielding an accurate, interpretable characterization of the target class. In addition, the CSP allows for a geometric interpretation of feasible regions in the feature space and the production of synthetic instances consistent with the constraints learned. Overall, the FIS-CSP-OM framework offers a powerful and interpretable approach for handling imbalanced classification problems by combining fuzzy logic, data mining, and constraint-based modeling. It opens new perspectives for explainable artificial intelligence, knowledge extraction, and constraint-driven data generation.
A. Al-Shaery, M. Roudani, Karim El Moutaouakil et al.· IEEE Access· 0 citations
