Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

Fuzzy systems show strong potential in explainable AI due to their rule-based architecture and linguistic variables. Existing approaches navigate the accuracy-explainability trade-off either through evolutionary multi-objective optimization (MOO), which is computationally expensive, or gradient-based scalarization, which cannot recover non-convex Pareto regions. We propose X-ANFIS, an alternating bi-objective gradient-based optimization scheme for explainable adaptive neuro-fuzzy inference systems. Cauchy membership functions are used for stable training under semantically controlled initializations, and a differentiable explainability objective is introduced and decoupled from the performance objective through alternating gradient passes. Validated in approximately 5,000 experiments on nine UCI regression datasets, X-ANFIS consistently achieves target distinguishability while maintaining competitive predictive accuracy, recovering solutions beyond the convex hull of the MOO Pareto front.

Interpretable Fuzzy Systems For Forward Osmosis Desalination

Preserving interpretability in fuzzy rule-based systems (FRBS) is vital for water treatment, where decisions impact public health. While structural interpretability has been addressed using multi-objective algorithms, semantic interpretability often suffers due to fuzzy sets with low distinguishability. We propose a human-in-the-loop approach for developing interpretable FRBS to predict forward osmosis desalination productivity. Our method integrates expert-driven grid partitioning for distinguishable membership functions, domain-guided feature engineering to reduce redundancy, and rule pruning based on firing strength. This approach achieved comparable predictive performance to cluster-based FRBS while maintaining semantic interpretability and meeting structural complexity constraints, providing an explainable solution for water treatment applications.

Predictive Maintenance for Ultrafiltration Membranes Using Explainable Similarity-Based Prognostics

In reverse osmosis desalination, ultrafiltration (UF) membranes degrade due to fouling, leading to performance loss and costly downtime. Most plants rely on scheduled preventive maintenance, since existing predictive maintenance models, often based on opaque machine learning methods, lack interpretability and operator trust. This study proposes an explainable prognostic framework for UF membrane remaining useful life (RUL) estimation using fuzzy similarity reasoning. A physics-informed Health Index, derived from transmembrane pressure, flux, and resistance, captures degradation dynamics, which are then fuzzified via Gaussian membership functions. Using a similarity measure, the model identifies historical degradation trajectories resembling the current state and formulates RUL predictions as Takagi-Sugeno fuzzy rules. Each rule corresponds to a historical exemplar and contributes to a transparent, similarity-weighted RUL estimate. Tested on 12,528 operational cycles from an industrial-scale UF system, the framework achieved a mean absolute error of 4.50 cycles, while generating interpretable rule bases consistent with expert understanding.

Explainable Uncertainty Quantification for Wastewater Treatment Energy Prediction via Interval Type-2 Neuro-Fuzzy System

Wastewater treatment plants consume 1-3% of global electricity, making accurate energy forecasting critical for operational optimization and sustainability. While machine learning models provide point predictions, they lack explainable uncertainty quantification essential for risk-aware decision-making in safety-critical infrastructure. This study develops an Interval Type-2 Adaptive Neuro-Fuzzy Inference System (IT2-ANFIS) that generates interpretable prediction intervals through fuzzy rule structures. Unlike black-box probabilistic methods, the proposed framework decomposes uncertainty across three levels: feature-level, footprint of uncertainty identify which variables introduce ambiguity, rule-level analysis reveals confidence in local models, and instance-level intervals quantify overall prediction uncertainty. Validated on Melbourne Water's Eastern Treatment Plant dataset, IT2-ANFIS achieves comparable predictive performance to first order ANFIS with substantially reduced variance across training runs, while providing explainable uncertainty estimates that link prediction confidence directly to operational conditions and input variables.

Explainable Fuzzy GNNs for Leak Detection in Water Distribution Networks

Timely leak detection in water distribution networks is critical for conserving resources and maintaining operational efficiency. Although Graph Neural Networks (GNNs) excel at capturing spatial-temporal dependencies in sensor data, their black-box nature and the limited work on graph-based explainable models for water networks hinder practical adoption. We propose an explainable GNN framework that integrates mutual information to identify critical network regions and fuzzy logic to provide clear, rule-based explanations for node classification tasks. After benchmarking several GNN architectures, we selected the generalized graph convolution network (GENConv) for its superior performance and developed a fuzzy-enhanced variant that offers intuitive explanations for classified leak locations. Our fuzzy graph neural network (FGENConv) achieved Graph F1 scores of 0.889 for detection and 0.814 for localization, slightly below the crisp GENConv 0.938 and 0.858, respectively. Yet it compensates by providing spatially localized, fuzzy rule-based explanations. By striking the right balance between precision and explainability, the proposed fuzzy network could enable hydraulic engineers to validate predicted leak locations, conserve human resources, and optimize maintenance strategies. The code is available at github.com/pasqualedem/GNNLeakDetection.