Abstract
The equivalence between differential equation models and fuzzy logic models is demonstrated for a certain family of fuzzy systems—those which use fuzzy spline wavelets as membership functions. The universal approximation property of fuzzy systems built with spline wavelets is exploited for replacing operational representations of differential equations with sparse matrix equations. The solution of the matrix equations 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 systems. The proposed method enjoys the excellent numerical and computational characteristics of the fast wavelet transform.
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