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In this paper, a new control approach is proposed for the synchronization and stabilization of a class of chaotic systems with unknown dynamics and input nonlinearities. Type-3 fuzzy logic systems (T3-FLSs) are developed to adaptively model the dynamics of both master and slave systems in real time. The input is affected by sector-bounded hysteresis and quantization, and these challenges are explicitly addressed in the control design. Unlike conventional methods, the proposed strategy does not require prior knowledge of the system equations or the derivatives of system signals. The adaptation laws for the T3-FLS parameters and estimation errors are rigorously derived using stability and robustness analysis, ensuring smooth control signals without chattering. Extensive simulations and real-time examinations demonstrate that the method achieves accurate synchronization even under severe uncertainties, high levels of random noise, and non-identical chaotic systems. Comparative results confirm the superiority of the proposed approach over existing fuzzy control methods.