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.