Approximation capabilities of multilayer fuzzy neural networks on the set of fuzzy-valued functions

This paper first introduces a piecewise linear interpolation method for fuzzy-valued functions. Based on this, we present a concrete approximation procedure to show the capability of four-layer regular fuzzy neural networks to perform approximation on the set of all image continuous fuzzy-valued functions. This approach can also be used to approximate image continuous fuzzy-valued functions. An example is given to illustrate the approximation procedure.