Differentiating adaptive Neuro-Fuzzy Inference System for accurate function derivative approximation

Function and its partial derivative approximation based upon a set of discrete dataset are important issues in soft computing. Several function approximators have been presented most of them fits a model to the dataset so that the Mean Squared Error is minimized. In this paper, we propose to calculate the derivative of the Neuro-Fuzzy function approximator directly according to the parametric structure of the system and the available dataset. A criterion for derivative approximation is defined based on a combination of MSE and Approximate Entropy. According to this criterion, the superiority of the Neuro-Fuzzy model is demonstrated in comparison with some other types of Artificial Neural Networks and Polynomial models.