Fuzzy controllers design using space-filling curves

Abstract

We present a clustering technique for fuzzy rules based on Hilbert space-filling curves (SFC). SFC scans an n-dimensional space and reduces it to a curve, i.e. a one-dimensional line. We first introduce the Hilbert space-filling curves, and outline the algorithms for clustering and adaptive clustering which demonstrate SFC efficient self-organizing features. We then propose a SFC fuzzy inference model based on clustering the object space. The SFC fuzzy model is then used to design a fuzzy controller. The proposed method achieves a dramatic reduction of the complexity of fuzzy controller by reducing the multivariable fuzzification problem to a one dimensional space.