Summary: This paper addresses an adaptive fuzzy prescribed performance synchronization for a class of uncertain non-strict feedback chaotic systems subject to input quantization and time-varying actuator faults. The proposed approach utilizes fuzzy logic systems to estimate uncertainties. In addition, multiplicative and additive faults are considered simultaneously, which may occur either separately or simultaneously. To address the challenge, based on the backstepping scheme and a filter, an intermediate controller is conducted to compensate for the interference between actuator faults and quantification, in which a damping term and a positive time-varying function are introduced. Moreover, treating the error system as a constrained system, a simplified nonlinear mapping is employed to achieve asymmetric prescribed performance synchronization. Unlike traditional methods that rely on barrier Lyapunov functions and switch functions, the proposed approach eliminates the need for a switch function and extends the action scope to cover all synchronization errors. The analysis demonstrates that even if actuator faults and input quantization coexist, all signals in the closed-loop system remain bounded, and synchronization errors remain within the prescribed performance range. Finally, synchronization simulations are conducted on a nonlinear gyroscope system and a non-autonomous chaotic micro-electro-mechanical system to reveal the validity of the proposed scheme.