A study on multi-layer fuzzy polynomial inference system based on an extended GMDH algorithm

A new design methodology is proposed to identify the structure and parameters of a fuzzy model using PNN and a fuzzy inference method. The PNN is the extended structure of the GMDH (Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and cubic besides the biquadratic polynomial used in the GMDH. The FPNN (Fuzzy Polynomial Neural Networks) algorithm uses PNN (Polynomial Neural network) structure and the fuzzy inference method. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here a regression polynomial inference is based on a consequence of fuzzy rules with polynomial equations such as linear, quadratic and cubic equations. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture. We consider a model that combines the advantage of both FPNN and PNN. Also we use the training and testing data set to obtain a balance between the approximation and generalization of the process model. Several numerical examples are used to evaluate the performance of our proposed model.