y=f(x)where f represents the processing by the entire radial basis function neural network. Let x=[=,,x2,x].The input to the i receptive field unit is x, and its output is denoted with R;(x). It has what is called a"strength"which we denote by y,. Assume that there are M receptive field units. Hence, from Figure 4.3, y=f(x)=∑R(x) is the output of the radial basis function neural network y Figure 4.3 Radial basis function neural network model There are several possible choices for the"receptive field units"Ri(x) R(x) Wherec-[ci ci.ciI, o, is a scalar, and if: is a vector then==V== 2. We could choose R(x) where c and o. are defined in choice 1 There are also alternatives to how to compute the output of the radial basis function neural network. For instance rather than computing the simple sum as in Equation(4.3), you could compute a weighted average y, R() y=f(x)=M (44) ∑R(x) It is also possible to define multilayer radial basis function neural networks This completes the definition of the radial basis function neural network. Next, we explain the relationships between multilayer perceptions and radial basis function neural networks and fuzzy systems 4.3.3 Relations hips between Fuzzy Systems and Neural Networks There are two ways in which there are relationships between fuzzy systems and neural networks. First, techniques from one area can be used in the other. Second, in some cases the functionality(i.e, the nonlinear function that they PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cny =f(x) where f represents the processing by the entire radial basis function neural network. Let [ 1 2 , , ] T n x = x x x  . The input to the i th receptive field unit is x, and its output is denoted with Ri (x). lt has what is called a "strength" which we denote by i y . Assume that there are M receptive field units. Hence, from Figure 4.3, ( ) ( ) 1 M i i i y f x y R x = = = å (4.3) is the output of the radial basis function neural network. Figure 4.3 Radial basis function neural network model. There are several possible choices for the "receptive field units" R i (x): 1. We could choose ( ) 2 2 exp i i i x c R x s æ ö - = ç- ÷ ç ÷ è ø Where 1 2 , , T i i i i n c = é ù c c c ë û  ,si is a scalar, and if z is a vector then T z = z z . 2. We could choose ( ) 2 2 1 1 exp i i i R x x c s = æ ö - + -ç ÷ ç ÷ è ø where i i c and s are defined in choice 1. There are also alternatives to how to compute the output of the radial basis function neural network. For instance, rather than computing the simple sum as in Equation (4.3), you could compute a weighted average ( ) ( ) ( ) 1 1 M i i i M i i y R x y f x R x = = = = å å （4.4） It is also possible to define multilayer radial basis function neural networks. This completes the definition of the radial basis function neural network. Next, we explain the relationships between multilayer perceptions and radial basis function neural networks and fuzzy systems. 4.3.3 Relationships Between Fuzzy Systems and Neural Networks There are two ways in which there are relationships between fuzzy systems and neural networks. First, techniques from one area can be used in the other. Second, in some cases the functionality (i.e., the nonlinear function that they PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn