THE FUZZY RULE-BASE SOLUTION OF DIFFERENTIAL-EQUATIONS

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.