Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

2026-02-22

AI Summary

This work addresses the longstanding challenge in neural fuzzy systems of achieving an effective trade-off between predictive accuracy and interpretability, compounded by the inability of conventional multi-objective optimization methods to adequately cover non-convex Pareto fronts. To overcome these limitations, the authors propose X-ANFIS, a novel framework that introduces a differentiable interpretability objective and employs an alternating bi-objective gradient optimization strategy to decouple the optimization of performance and interpretability. By integrating semantic initialization based on Cauchy membership functions with an adaptive neuro-fuzzy inference mechanism, X-ANFIS consistently achieves high predictive accuracy and strong interpretability across nine UCI regression datasets. Extensive validation through approximately 5,000 experiments demonstrates that the method not only stabilizes this dual-objective balance but also discovers Pareto-optimal solutions beyond the convex hull of traditional approaches.

Technology Category

• Humans and AI: Explainable AI (XAI) for Human Understanding
• Machine Learning: Transparent, Interpretable, Explainable ML
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• explainable AI
• accuracy-explainability trade-off
• Pareto front
• neuro-fuzzy systems
• multi-objective optimization

Innovation

• explainable AI
• neuro-fuzzy systems
• bi-objective optimization
• differentiable explainability
• Cauchy membership functions