Multi - Variable Fuzzy Systems By Fourier Series Decomposition

| This paper presents a novel method of automatically generating a multi-variable fuzzy inference system from given sample sets. The method exploits the Fourier series expansion in decomposing the sample sets into simpliied tasks of generating a fuzzy system with a single input variable independent of the other variables. Once the single input fuzzy systems are obtained, the resulting decomposed fuzzy rules and membership functions for all the variables are composed and integrated back into the fuzzy system appropriate for the original sample set requiring only a moderate cost of computation. Compared with the power series expansion method we used in PolyNeu-Fuz 6] and ParNeuFuz 5], the distinct advantage of the present Fourier method lies in obtaining a stable fuzzy system by retaining any speciied accuracy of the resulting multivariable function on the original sample set because we can make a full use of error bound analysis available at each of the construction steps.