The interpolation property of fuzzy polynomial approximation

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function memberships are used. The fuzzy inference procedure combines two polynomials of degree n-1 and m-1 in x into one single polynomial of at most degree max(n, m) which passes through the points of intersections of the original polynomials. The conditions for the degeneration case is also discussed