This study has been studied SIRMs (Single Input Rule Modules) connected fuzzy inference model in order to provide the insight into fuzzy control systems. The framework consists of two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy controller) which are selected out of continuous function space is compact metrizable. And assuming approximate reasoning to be a functional on the set of membership functions, its continuity is proved. Then, we show the existence of SIRMs which minimize (maximize) the integral performance function of the nonlinear feedback fuzzy system.
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