implement) is identical. Some label the intersection between fuzzy systems and neural networks with the term fuzzy-neural"or "neuro-fuzzy"to highlight that techniques from both fields are being used. Here, we avoid this terminology and simply highlight the basic relationships between the two fields Multilayer Perceptrons The multilayer perceptron should be viewed as a nonlinear network whose nonlinearity can be tuned by changing the weights, biases, and parameters of the activation functions. The fuzzy system is also a tunable nonlinearity whose shape can be changed by tuning, for example, the membership functions. Since both are tunable nonlinearities, the following approaches are possible Gradient methods can be used for training neural networks to perform system identification or to act estimators or predictors in the same way as fuzzy systems were trained. Indeed, the gradient training of neural networks, called"back-propagation training, " was introduced well before the gradient training of fuzzy systems, and the idea for training fuzzy systems this way came from the field of neural networks a Hybrid methods for training can also be used for neural networks. For instance, gradient methods may be used in conjunction with clustering methods applied to neural networks a Indirect adaptive control can also be achieved with a multilayer perceptron. To do this we use two multilayer perceptrons as the tunable nonlinearities in the certainty equivalence control law and the gradient method for tuning a Gain scheduled control may be achieved by training a multilayer perceptron to map the associations between operating conditions and controller parameters This list is by no means exhaustive. It simply shows that multilayer perceptron networks can take on a similar role to that of a fuzzy system in performing the function of being a tunable nonlinearity. An advantage that the fuzzy system may have, however, is that it often facilitates the incorporation of heuristic knowledge into the solution to the problem, which can, at times, have a significant impact on the quality of the solution Radial basis function neural Networks Some radial basis function neural networks are equivalent to some standard fuzzy systems in the sense that they are functionally equivalent (i.e, given the same inputs, they will produce the same outputs). To see this, suppose that in Equation(4.4)we let M=R(i.e, the number of receptive field units equal to the number of rules),)i=Di(i.e,the receptive field unit strengths equal to the output membership function centers), and choose the receptive field units as R(x)=1(x) (.e, choose the receptive field units to be the same as the premise membership functions). In this case we see that the radial basis function neural network is identical to a certain fuzzy system that uses center-average defuzzification. Thi fuzzy system is then given by y=/(x)=2=9(x) ∑A1(x) It is also interesting to note that the functional fuzzy system( the more general version of the Takagi-Sugeno fuzzy system) is equivalent to a class of two-layer neural networks 2001 The equivalence between this type of fuzzy system and a radial basis function neural network shows that all the hniques in this book for the above type of fuzzy system work in the same way for the above type of radial basis function neural network(or, using[2001, the techniques for the Takagi-Sugeno fuzzy system can be used for a type of multilayer radial basis function neural network) PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cnimplement) is identical. Some label the intersection between fuzzy systems and neural networks with the term "fuzzy-neural" or "neuro-fuzzy" to highlight that techniques from both fields are being used. Here, we avoid this terminology and simply highlight the basic relationships between the two fields. Multilayer Perceptrons The multilayer perceptron should be viewed as a nonlinear network whose nonlinearity can be tuned by changing the weights, biases, and parameters of the activation functions. The fuzzy system is also a tunable nonlinearity whose shape can be changed by tuning, for example, the membership functions. Since both are tunable nonlinearities, the following approaches are possible: ¡ Gradient methods can be used for training neural networks to perform system identification or to act as estimators or predictors in the same way as fuzzy systems were trained. Indeed, the gradient training of neural networks, called "back-propagation training," was introduced well before the gradient training of fuzzy systems, and the idea for training fuzzy systems this way came from the field of neural networks. ¡ Hybrid methods for training can also be used for neural networks. For instance, gradient methods may be used in conjunction with clustering methods applied to neural networks. ¡ Indirect adaptive control can also be achieved with a multilayer perceptron. To do this we use two multilayer perceptrons as the tunable nonlinearities in the certainty equivalence control law and the gradient method for tuning. ¡ Gain scheduled control may be achieved by training a multilayer perceptron to map the associations between operating conditions and controller parameters. This list is by no means exhaustive. It simply shows that multilayer perceptron networks can take on a similar role to that of a fuzzy system in performing the function of being a tunable nonlinearity. An advantage that the fuzzy system may have, however, is that it often facilitates the incorporation of heuristic knowledge into the solution to the problem, which can, at times, have a significant impact on the quality of the solution. Radial Basis Function Neural Networks Some radial basis function neural networks are equivalent to some standard fuzzy systems in the sense that they are functionally equivalent (i.e., given the same inputs, they will produce the same outputs). To see this, suppose that in Equation (4.4) we let M =R (i.e., the number of receptive field units equal to the number of rules), i i y b = (i.e., the receptive field unit strengths equal to the output membership function centers), and choose the receptive field units as ( ) ( ) Ri i x x = m (i.e., choose the receptive field units to be the same as the premise membership functions). In this case we see that the radial basis function neural network is identical to a certain fuzzy system that uses center-average defuzzification. This fuzzy system is then given by 1 1 ( ) ( ) ( ) R i i i R i i b x y f x x m m = = = = å å It is also interesting to note that the functional fuzzy system (the more general version of the Takagi-Sugeno fuzzy system) is equivalent to a class of two-layer neural networks [200]. The equivalence between this type of fuzzy system and a radial basis function neural network shows that all the techniques in this book for the above type of fuzzy system work in the same way for the above type of radial basis function neural network (or, using [200], the techniques for the Takagi-Sugeno fuzzy system can be used for a type of multilayer radial basis function neural network). PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn