Armin Shmilovici Leib

Based on the fact that fuzzy systems can be represented as a linear combination of fuzzy basis functions (FBF), it is proposed that spline wavelets scaling functions, will be used as FBF. A fuzzy system built from dilations and translations of a wavelet scaling function can universally approximate any function in a Hilbert space. Such fuzzy systems would also enjoy the excellent numerical and computational characteristics of the fast wavelet transform, while retaining the approximation properties of spline functions.