Robust regression based training of ANFIS

The Adaptive Neuro Fuzzy Inference System (ANFIS) is an attractive compromise between the adaptability of a neural network and the interpretability of a fuzzy inference system. Typically, the membership functions of some of the variables can be determined a priori based on domain knowledge. Membership functions of the other variables are adapted using a hybrid learning rule. The hybrid learning rule is based on a decomposition of the parameter set and learning is based on interleaving of two phases. In one phase, the consequent parameters are adjusted using a least squares algorithm, assuming the premise parameters are fixed. In the second phase the premise parameters are adjusted using gradient descent, assuming the consequent parameters are fixed. However, the least squares algorithm used in adjusting the consequent parameters is susceptible to outliers and often leads to premise parameters (membership functions) that are less meaningful. We study this effect using noisy data sets and propose a hybrid learning algorithm based on robust regression for training the ANFIS.