Robust hybrid learning approach for adaptive neuro-fuzzy inference systems

The Adaptive Neuro-Fuzzy Inference System (ANFIS) is a regression model that uses fuzzy logic and neural networks, making it suitable for modeling the uncertainty of regression problems. However, the non -robust loss function in ANFIS's hybrid learning algorithm can make it susceptible to the direct effects of noise and outliers. This paper introduces a new procedure that uses robust loss functions to enhance the hybrid learning performance against noise and outliers. In addition, a new robust loss function is devised that can completely ignore outliers. Furthermore, a set of robust loss functions with mathematical relations are suggested. The proposed approach is evaluated on real -world problems, including weather forecasting and stock market prediction. Results suggested that the proposed model can reduce the Mean Square Error (MSE) in regression. Moreover, the new procedure enables utilizing different loss functions based on the application.