Design of fuzzy system with linear bounds

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 and linearly bounded function in its output can be approximated with any degree of accuracy by the fuzzy system formed with the above fuzzy sets and conditions.