HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry
This work provides an incremental improvement for researchers and practitioners using ANFIS for tasks requiring transparent reasoning and improved predictive accuracy.
This paper proposes HyperANFIS, a hyperbolic extension of the Adaptive Neuro-Fuzzy Inference System (ANFIS), to improve representational capacity and predictive performance by performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. HyperANFIS consistently outperforms the standard ANFIS baseline and its variants across all datasets, while also generating higher-quality fuzzy rules.
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.