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The paper introduces xFODE+, an interpretable system identification model that combines Fuzzy Additive ODEs with Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) to produce prediction intervals (PIs) and point predictions. By constraining membership functions to activate only neighboring rules, xFODE+ enhances local transparency and interpretability compared to standard Fuzzy ODEs. Experiments on benchmark datasets demonstrate that xFODE+ achieves comparable accuracy and PI quality to FODE, while offering improved interpretability of the model's internal states.
Finally, a system identification model that gives you both accurate predictions *and* interpretable uncertainty estimates.
Recent advances in Deep Learning (DL) have boosted data-driven System Identification (SysID), but reliable use requires Uncertainty Quantification (UQ) alongside accurate predictions. Although UQ-capable models such as Fuzzy ODE (FODE) can produce Prediction Intervals (PIs), they offer limited interpretability. We introduce Explainable Type-2 Fuzzy Additive ODEs for UQ (xFODE+), an interpretable SysID model which produces PIs alongside point predictions while retaining physically meaningful incremental states. xFODE+ implements each fuzzy additive model with Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) and constraints membership functions to the activation of two neighboring rules, limiting overlap and keeping inference locally transparent. The type-reduced sets produced by the IT2-FLSs are aggregated to construct the state update together with the PIs. The model is trained in a DL framework via a composite loss that jointly optimizes prediction accuracy and PI quality. Results on benchmark SysID datasets show that xFODE+ matches FODE in PI quality and achieves comparable accuracy, while providing interpretability.