Levenberg marquardt algorithm for the training of type-2 fuzzy neuro systems with a novel type-2 fuzzy membership function

A new training approach based on the Levenberg-Marquardt algorithm is proposed for type-2 fuzzy neural networks. While conventional gradient descent algorithms use only the first order derivative, the proposed algorithm used in this paper benefits from the first and the second order derivatives which makes the training procedure faster. Besides, this approach is more robust than the other techniques that use the second order derivatives, e.g. Gauss-Newton´s method. The training algorithm proposed is tested on the training of a type-2 fuzzy neural network used for the prediction of a chaotic Mackey-Glass time series. The results show that the learning algorithm proposed not only results in faster training but also in a better forecasting accuracy.