Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications

Abstract

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy. A formula to compute the lower upper bounds on the number of interval-valued fuzzy sets needed to achieve a pre-specified approximation accuracy for an arbitrary multivariate continuous<br />function is then presented. In addition, a method to design the interval-valued<br /> fuzzy systems based on $R$- and $S$-implications in order to approximate a given continuous<br />function with a required approximation accuracy is represented. Finally, two numerical examples are provided to illustrate the proposed procedure.