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

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.