Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

A team of researchers has introduced X-ANFIS, a novel method for building AI systems that are both accurate and interpretable. The core challenge in explainable AI (XAI) is the inherent trade-off between a model's predictive performance and its transparency. Existing approaches, like evolutionary multi-objective optimization, are computationally expensive, while gradient-based methods often miss optimal solutions in non-convex regions. X-ANFIS proposes an alternating bi-objective gradient-based optimization scheme specifically for Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which are inherently more interpretable due to their rule-based, fuzzy logic architecture.

The technical innovation lies in its two-part approach. First, it uses Cauchy membership functions, which provide more stable training under semantically controlled initializations of the fuzzy rules. Second, and most crucially, it introduces a differentiable explainability objective that is mathematically decoupled from the standard performance (accuracy) objective. The optimization alternates gradient update passes between these two objectives, allowing the system to navigate the trade-off landscape more effectively than single-objective scalarization.

The method was rigorously validated in approximately 5,000 experiments on nine standard UCI regression datasets. The results show that X-ANFIS consistently achieves a pre-defined target level of 'distinguishability'—a measure of how clear and separable the learned fuzzy rules are—while maintaining predictive accuracy competitive with less explainable models. A significant finding is that the method can recover solutions that lie beyond the convex hull of the Pareto front found by traditional multi-objective optimization, meaning it discovers better compromise solutions that were previously inaccessible. The work has been accepted for presentation at the IEEE Conference on Artificial Intelligence 2026.