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Fuzzification Using Space-Filling Curves

Abstract This paper introduces the Hilbert Space-Filling Curves SFC and outlines algorithms, which demonstrate the SFC efficient self-organizing features. We then propose a SFC fuzzy model based on clustering the object space. The SFC fuzzy model is utilized to construct a fuzzy feedback controller. It is shown that the self-replicating feature of SFC can be utilized to construct successively improving control strategies based on symmetric decision trees. The proposed SFC technique achieves a dramatic reduction in the complexity of fuzzy controllers by reducing the multi-dimensional fuzzification problem to aone-dimensional space.