Adaptive Neuro-Fuzzy Inference System with second order Sugeno consequents

Adaptive Neuro-Fuzzy Inference System (ANFIS) with first order Sugeno consequent is used widely in modeling applications. Though it has the advantage of giving good modeling results in many cases, it is not capable of modeling highly non-linear systems with high accuracy. In this paper, an efficient way for using ANFIS with Sugeno second order consequents is presented. Better approximation capability of Sugeno second order consequents compared to lower order Sugeno consequents is shown. Subtractive clustering is used to determine the number and type of membership functions. A hybrid-learning algorithm that combines the gradient descent method and the least squares estimate is then used to update the parameters of the proposed Second Order Sugeno-ANFIS (SOS-ANFIS). Simulation of the proposed SOS-ANFIS for two examples shows better results than that of lower order Sugeno consequents. The proposed SOS-ANFIS shows better initial error, better convergence, quicker convergence and much better final error value.