Interpretable Fuzzy Hyperbolic Networks
提出可解释模糊双曲网络，通过非对称隶属函数和子规则保持输入变量与模糊规则的直接对应，在多个函数逼近基准上相比传统模型提升了可解释性且精度相当。
Achieving interpretability remains an elusive challenge for nonlinear system models due to the inherent tradeoff between accuracy and transparency. Classical analytical methods often provide clearer physical insight, whereas data-driven models such as artificial neural networks (ANNs) offer strong predictive performance but limited interpretability and less explicit uncertainty representation. This article proposes an interpretable fuzzy hyperbolic network (IFHN) that addresses these concerns. By introducing asymmetric right and left membership functions (RMF and LMF) together with subrules defined directly in the original input space, the proposed framework eliminates the need for input-space generalization. The resulting fuzzy inference system yields a separately connected neural architecture that preserves a direct correspondence among input variables, subnetworks, and extracted fuzzy rules. Consequently, IFHN combines the learning capability of neural networks with the transparency of fuzzy reasoning. From a theoretical perspective, IFHN inherits the approximation capability of single-hidden-layer hyperbolic tangent networks in the single-input case and yields an additive approximation model in the multi-input case. In addition, a structural interpretability index is proposed to support quantitative comparison of model transparency, and a backpropagation algorithm is employed to learn both antecedent and consequent parameters. The proposed model is evaluated on several function-approximation benchmark problems, including the sine function, increasing sine function, quadratic Hermite function, nonlinear functions, generalized sine-sum, and a real-world Servo regression dataset. The results demonstrate that IFHN provides improved interpretability while maintaining competitive approximation accuracy compared with the traditional generalized fuzzy hyperbolic model (GFHM) and a fully connected ANN, thereby establishing it as a promising framework for interpretable nonlinear system modeling.