Parameter conditions for monotonic Takagi-Sugeno-Kang fuzzy system

This paper presents sufficient conditions on the parameters of the Takagi-Sugeno-Kang (TSK) fuzzy system under which the output of the TSK fuzzy system becomes monotonic with respect to its input. The output of the TSK fuzzy system is first differentiated with respect to its input and the parameter conditions are derived so as to make the derivative nonnegative. The parameter conditions are developed for both single-input and multi-input TSK fuzzy systems where the involved fuzzy membership functions are differentiable everywhere or bar some finite points. The derived monotonicity conditions consist of two parts: the conditions on the consequent parts and the conditions on the fuzzy membership functions. They are further characterized for the most important types of fuzzy membership functions.

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