HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry

2026-08-12

AI Summary

This work proposes a novel extension of the adaptive neuro-fuzzy inference system (ANFIS) by integrating hyperbolic geometry into its architecture. Traditional ANFIS, constrained by the representational limitations of Euclidean space, struggles to adequately model complex data structures. To address this, the proposed method performs fuzzy rule prototype learning, rule activation, and consequent aggregation entirely within hyperbolic space, while preserving ANFIS’s interpretable IF-THEN rule generation mechanism. This approach substantially enhances rule representation capacity, inter-rule collaboration, and the reliability of generated rules without compromising model transparency. Empirical evaluations demonstrate that the hyperbolic ANFIS consistently outperforms standard ANFIS and its variants across multiple datasets, yielding higher-quality interpretable fuzzy rules.

Abstract

The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.

Problem

• ANFIS
• rule representation
• interpretability
• hyperbolic geometry
• fuzzy inference

Innovation

• Hyperbolic geometry
• ANFIS
• Interpretable AI
• Fuzzy rule representation
• Neuro-fuzzy systems