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This paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the IF-parts, but used only in the THEN-parts of the fuzzy rules of the current layer.The proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier.From the simulation of ball and beam control system, it is demonstrated that the proposed scheme approximates with good accuracy the model nonlinear controller with fewer fuzzy rules than the centralized fuzzy system and its control performance is comparable to that of the nonlinear controller. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]