Sufficient and necessary conditions for Boolean fuzzy systems as universal approximators

A formula is first presented to compute the lower upper bounds on the number of fuzzy sets to achieve pre-specified approximation accuracy for an arbitrary multivariate continuous function. The necessary condition for Boolean fuzzy systems as universal approximators with minimal system configurations is then discussed. Two examples are provided to demonstrate how to design a Boolean fuzzy system in order to approximate a given continuous function with a required approximation accuracy.