Statistical features and robustness of chaotic fuzzy maps

The properties of the discrete-time nonlinear dynamics induced by a fuzzy system are investigated. Nonlinear dynamical system theory tools are applied to give conditions for fuzzy maps to produce sufficiently complex but asymptotically definite behavior and an approximation scheme allowing its statistical characterization is discussed. Then, to allow the application of synthesis and implementation methodologies for fuzzy systems to the realization of nontrivial or even chaotic dynamics we also give a novel and effective result on the robustness of that statistical characterization with respect to small perturbations or to certain implementation non-idealities.