The equivalence between differential equation models and fuzzy logic m
odels is demonstrated for a certain family of fuzzy systems-those whic
h use fuzzy spline 'wavelets as membership functions. The universal ap
proximation property of fuzzy systems built with spline wavelets is ex
ploited for replacing operational representations of differential equa
tions with sparse matrix equations. The solution of the matrix equatio
ns has a direct interpretation as a set of fuzzy rules. The fuzzy rule
base thus generated provides an approximate solution to the original
differential equation while retaining the explanatory power of fuzzy s
ystems. The proposed method enjoys the excellent numerical and computa
tional characteristics of the fast wavelet transform.