Overview While up to this point we have focused on control, in this chapter we will examine how to use fuzzy systems for estimation and identification. The basic problem to be studied here is how to construct a fuzzy system from numerical data. This is in contrast to our discussion in Chapters 2 and 3, where we used linguistics as the starting point to specify a fuzzy system. If the numerical data is plant input-output data obtained from an experiment, we may identify a fuzzy system model of the plant. This may be useful for simulation purposes and sometimes for use in a controller. On the other hand, the data e from other sources, and a fuzzy system may be used to provide for a parameterized nonlinear function that fits the data by using its basic interpolation capabilities. For instance, suppose that we have a human expert who controls some process and we observe how she or he does this by observing what numerical plant input the expert picks for the given numerical data that she or he observes. Suppose further that we have many such associations between "decision-making data." The methods in this chapter will show how to construct rules for a fuzzy controller from this data (., identify a controller from the human-generated decision-making data), and in this sense they provide another method to design controllers. Yet another problem that can be solved with the methods in this chapter is that of how to construct a fuzzy system that will serve as a parameter estimator. To do this, we need data that shows, roughly how the input-output mapping of the estimator should behave
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