<p>This work investigates fuzzy adaptive output-feedback control issue for incommensurate fractional-order nonlinear systems with input and output quantization. The input and output are quantized via a sector bounded quantizer. Due to the case that system states are partially measurable, a fuzzy state observer with quantized signals is constructed. Fuzzy logic systems are employed to model the nonlinear dynamics. Further, the fractional-order dynamic surface control strategy is developed to overcome the complexity brought by adaptive backstepping technique. Then, for the purpose of ensuring the boundability of a series of errors caused by continuous original state in stability analysis and discontinuous quantization state in control, a novel fractional-order projection operator with smooth property is proposed. Finally, by means of the frequency distribution model and indirect Lyapunov method, it is proved that all closed-loop signals are bounded. The advantages of the proposed control method are illustrated by a numerical example.</p>