Journal of American Science, 2010;6(12) http://www.americanscience.org A modified Algorithm to Model Highly Nonlinear System Tharwat O. S. Hanafy Al_Azhar University,Faculty of Engineering, Systems and Computers Department s_ewiss@yahoo.com Abstract: In this paper, the Fusion of neural and fuzzy Systems will be investigated. Membership Function Generation and its mapping to Neural Network are introduced. An adaptive network fuzzy inference system (ANFIS) is introduced, and Multiple Inputs /Outputs Systems (Extended ANFIS Algorithm) is implemented. A Modification algorithm of ANFIS, Coupling of ANFIS called coactive neuro fuzzy system (CANFIS), is introduced and implemented using Matlab. The software of the modified algorithm of MIMO model identification is built. To test the validity of the modified algorithm ANFIS (CANFIS algorithm), an example is simulated from the numerical equation. The result of modified algorithm (CANFIS) showed a conformance with the simulated example and the root mean square (RMSE) is very small. [Tharwat O. S. Hanafy. A modified Algorithm to Model Highly Nonlinear System. Journal of American Science 2010;6(12):747-759]. (ISSN: 1545-1003). http://www.americanscience.org . Keywords: A modified Algorithm to Model Highly Nonlinear System 1. Introduction: Fuzzy logic was first developed by Zadeh [1] in the mid-1960s for representing uncertain and imprecise knowledge. It provides an approximate but effective means of describing the behavior of systems that are too complex, ill-defined, or not easily analyzed mathematically. Fuzzy variables are processed using a system called a fuzzy logic controller. It involves fuzzification, fuzzy inference, and defuzzification[2]. An adaptive network fuzzy inference system is investigated. In this paper we will introduce two different learning algorithms. Also, Multiple Inputs /Outputs Systems (Extended ANFIS Algorithm) is implemented using two methods. Modification algorithm, Coupling of ANFIS is called coactive neuro fuzzy system (CANFIS), is introduced and implemented using Matlab. Also, software for modification algorithm for MIMO is built. To test the validity of the modified algorithm ANFIS (CANFIS) algorithm, an example is simulated from the numerical equation[3]. This paper organized seven sections. The first section is introduction. The structure of neuro fuzzy systems is introduced in section 2. The generating fuzzy rules are investigated in section three. Two different ANFIS learning algorithm presented in section four. The modified algorithm (CANFIS) is introduced in section five. Section six introduced conclusion. 2. Neural Fuzzy Systems In order to process fuzzy rules by neural networks, it is necessary to modify the standard neural network structure appropriately [2]. Since fuzzy systems are universal approximators, it is expected that their equivalent neural network representations will posses the same property. The reason to represent a fuzzy system in terms of neural network is to utilize the learning capability of neural networks to improve performance, such as adaptation of fuzzy systems. Thus, the training algorithm in the modified neural networks should be examined. 2.1 Membership Function Generation A generalized bell membership function, commonly referred to as bell MF, is characterized by three parameters namely a, b, c. }, ] ) [( exp{ ) ( 2 1 i b i i Ai a c x x     (1) A desired, generalized bell membership function can be obtained with the proper selection of the parameters a, b, c. The parameters a and c represent the width and the center of the bell function, and b represents the slopes at the crossover points. Various other membership functions such as triangular, trapezoidal, Gaussian, and sigmoidal can be used in the formulation of membership functions [3]. The triangular and trapezoidal membership functions, due to their simplicity and computational efficiency, are used extensively in the formulation of membership functions (MF) consist. The Gaussian, the generalized bell function, and the sigmoidal membership functions are smooth and nonlinear functions and are increasingly popular for specifying fuzzy sets. The generalized bell function has one parameter more than the Gaussian membership functions, resulting in an extra degree of freedom to adjust the steepness at the crossover points [4]. The reason to represent a fuzzy system in terms of a neural network is to utilize the learning http://www.americanscience.org editor@americanscience.org 747