Interval type-2 Boolean fuzzy systems are universal approximators

Unlike the Mamdani and TS fuzzy systems, a Boolean fuzzy system, type-1 or type-2, employs a fuzzy implication to interpret its rules. There exist three families of type-2 fuzzy implications-R-implication, S-implication and QL-implication. In this paper, using the same technique that we developed previously [22, 23], we constructively prove that all the interval type-2 Boolean fuzzy systems, regardless of the implication they use, are universal approximators in that they are capable of uniformly approximating any real multivariate continuous function on a compact domain to any degree of accuracy.