Single-input single-output convex fuzzy systems as universal approximators for single-input single-output convex functions

Authors:
Jinwook Kim;Jin S. Lee
Affiliations:
Department of Electrical Engineering, Pohang University of Science and Technology, Pohang, Korea;Department of Electrical Engineering, Pohang University of Science and Technology, Pohang, Korea
Venue:
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Year:
2009

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Abstract

This paper derives sufficient conditions for a single-input single-output fuzzy system whose output is convex with respect to its input. They are composed of two parts: the constraint on input membership functions and the constraint on the THEN parts of fuzzy rule base. And we prove in a constructive manner that any continuously differentiable single-input single-output convex function can be approximated with any degree of accuracy by a single-input single-output fuzzy system with the above conditions.