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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...
In this paper, we derive sufficient conditions under which the single-input single-output fuzzy system is bounded by linear functions in its output. If the fuzzy system is constructed with the complete and consistent fuzzy sets with trapezoid membership functions, we show that the derived conditions are simply the constraints on the consequent part parameters. Then we prove that any continuously differentiable...
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