The Fuzzy Rule-Number Estimation of T-S Fuzzy Models as Universal Approximators

In this paper, a supremum of the total numbers of fuzzy rules is obtained by employing the characteristics of the function in building a fuzzy model to approximate the function to achieve a given approximation accuracy. The basic idea is to take advantage of the presentation of mean square error to formulate the supremum of the total numbers of fuzzy rules. The supremum relates approximation accuracy, the measurement and dimension of the domain of function, and the derivative or circumflexion of the function. Further, the influence of membership functions on the total number of fuzzy rules of T-S fuzzy model is analyzed when T-S fuzzy model is applied to function approximation. Numerical examples are given to illustrate the ideas and results. Applications and potentials are discussed.