A Sugeno–multiplicative neuron hybrid system trained by differential evolution algorithm for time series forecasting

This paper proposes a novel hybrid neuro-fuzzy forecasting framework that integrates the interpretability of the Sugeno fuzzy inference system with the nonlinear modelling capability of a multiplicative neuron model. Unlike conventional Sugeno models that rely on linear consequents, the proposed approach replaces them with nonlinear multiplicative neuron structures, significantly enhancing representation power while preserving interpretability at the rule level. The model is trained using Differential Evolution to effectively optimize nonlinear parameters and avoid local minima. The proposed method is evaluated on real-world financial time series datasets (ERussell and ETH/USD) under multiple forecasting horizons (10, 20, and 30 steps ahead). Performance is assessed using root mean square error and mean absolute percentage error metrics. Experimental results demonstrate that the proposed model consistently outperforms classical Sugeno systems and several neural network-based approaches in both accuracy and stability, particularly under nonlinear and volatile conditions. These findings highlight the effectiveness of structurally enhancing Sugeno consequents for time series forecasting.