In this paper, we study the problem of robust fuzzy adaptive output feedback stabilization for a class of nonlinear systems with quantized input and output constraints. The system under consideration has these characteristics: unknown state mismatch uncertainties and unknown disturbances, and unknown measurement noises. By employing the output filtering transformation, the fuzzy logic system (FLS) approximator, the backstepping, and the high gain observer technique, a non-fragile robust fuzzy adaptive observer and a hyperbolic tangent adaptive controller are presented to guarantee that the closed-loop system is ultimately uniformly bounded and the output is constricted in a prescribed performance curve. The effectiveness of the scheme is verified by numerical simulations.