How to determine the minimum number of rules to achieve given accuracy

Fuzzy systems have been proved to be universal approximators, yet a large number of fuzzy rules may be needed for high approximation accuracy. In this paper, we consider how to determine the minimum number of fuzzy rules required in a fuzzy system for approximation to achieve a given accuracy and how to construct this fuzzy system when there are only a limited number of input-output data pairs of the unknown system. The key point is to partition the input space nonuniformly. In particular, a tunnel algorithm is utilized for the single-input case. Numerical examples are given to demonstrate the proposed idea and algorithm.