Abstract
A number of methods have been proposed in the literature for designing fuzzy systems from input-output data, but very little was done to study the performance of the methods from a rigorous mathematical point of view. In this paper, approximation bounds are established for two methods - the table look-up scheme and the clustering method. Detailed formulas are derived to give the error bound between the nonlinear function to be approximated and the fuzzy system designed using the method based on input-output data pairs. Modified versions are also proposed for the two methods such that the designed fuzzy systems are well-defined over the whole input domain.
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