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This paper introduces HyperANFIS, an innovative adaptation of the adaptive neuro-fuzzy inference system (ANFIS) that utilizes hyperbolic geometry to enhance rule representation and interpretability. By shifting the rule-prototype learning, rule activation, and consequent aggregation processes into hyperbolic space, HyperANFIS significantly improves predictive accuracy and inter-rule collaboration while maintaining the generation of interpretable IF-THEN rules. Experimental results demonstrate that HyperANFIS outperforms standard ANFIS and its variants across multiple datasets, showcasing its superior ability to produce high-quality fuzzy rules.
HyperANFIS boosts predictive accuracy and rule quality by leveraging hyperbolic geometry, outperforming traditional ANFIS models.
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.
