Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

TL;DR

This paper introduces X-ANFIS, a novel gradient-based bi-objective optimization method for neuro-fuzzy systems that balances accuracy and explainability more effectively than prior approaches, demonstrated through extensive experiments.

Contribution

X-ANFIS is the first alternating gradient-based bi-objective scheme for neuro-fuzzy systems that recovers non-convex Pareto solutions efficiently.

Findings

X-ANFIS consistently achieves target explainability and competitive accuracy.

It recovers solutions beyond the convex Pareto front.

Validated in 5,000 experiments on nine datasets.

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.