A note on universal approximation by hierarchical fuzzy systems
In neural networks, multivariable functions are built up by using single-variable functions to transform high-dimensional problems into low-dimensional ones. Here, starting from the same idea, it is shown, by means of a constructive proof, that any continuous function of an \(n\)-dimensional variable on a compact set can be approximated by a hierarchical fuzzy system. The fuzzy system considered here is not the standard one, but rather is an alternative one defined as a weighted combination of memberships functions.
scientific article; zbMATH DE number 1478247