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In order to solve the adaptive noise cancellation (ANC) problem, a new IIR-based fuzzy system is proposed in this paper. By virtue of its short-term memory embedded in the input layer and the IIR-based long-term memory in the consequent part, the proposed approach can handle nonlinear and dynamic ANC problems very well. It has the non-recurrent structure so that there is no feedback from the output layer to the input layer. Therefore, global stability analysis for the system is evitable. Moreover, the size of the networks is parsimonious because no extra input variables are introduced as the other recurrent networks did. Another significance of the proposed fuzzy system is that the system dynamics are implemented by the individual linear and transversal IIR filters in the consequent part of the fuzzy system. This makes mathematical analysis and practical applications feasible.