choose to adjust (i. e, f(x 0)) can have a significant impact on the ultimate accuracy of the approximator. For instance, it may be that a Takagi-Sugeno (or functional) fuzzy system will provide a better approximator than a standard fuzzy system for a particular application We think of f(x0)as a structure for an approximator that is parameterized by 6. In this chapter we will study the use of fuzz systems as approximators, and use a fuzzy system as the structure for the approximator. The choice of the parameter vector 0 depends on,for example, how many membership functions and rules you use. Generally you want enough membership functions and rules to be able to get good accuracy, but not too many since if your function is"overparameterized this can actually degrade approximation accuracy. Often, it is best if the structure of the approximator is based on some physical knowledge of the system, as we explain how to do in Section 3. 2. 4 on page 228 Finally, while in this book we focus primarily on fuzzy systems(or if you understand neural networks you will see that several of the methods of this chapter directly apply to those also), at times it may be beneficial to use other approximation structures such as neural networks polynomials, wavelets, or splines(see Section 3. 10 For Further Study on page 287) 3.2.2 Relation to ldentification estimation and prediction Many applications exist in the control and signal processing areas thatchoose to adjust (i.e., f (x θ)) can have a significant impact on the ultimate accuracy of the approximator. For instance, it may be that a Takagi-Sugeno (or functional) fuzzy system will provide a better approximator than a standard fuzzy system for a particular application. We think of f (x θ) as a structure for an approximator that is parameterized by θ . In this chapter we will study the use of fuzzy systems as approximators, and use a fuzzy system as the structure for the approximator. The choice of the parameter vector θ depends on, for example, how many membership functions and rules you use. Generally, you want enough membership functions and rules to be able to get good accuracy, but not too many since if your function is "overparameterized" this can actually degrade approximation accuracy. Often, it is best if the structure of the approximator is based on some physical knowledge of the system, as we explain how to do in Section 3.2.4 on page 228. Finally, while in this book we focus primarily on fuzzy systems (or, if you understand neural networks you will see that several of the methods of this chapter directly apply to those also), at times it may be beneficial to use other approximation structures such as neural networks, polynomials, wavelets, or splines (see Section 3.10 "For Further Study," on page 287). 3.2.2 Relation to Identification, Estimation, and Prediction Many applications exist in the control and signal processing areas that