Traditional Adaptive Cruise Control (ACC) systems often struggle to dynamically adapt to rapidly changing traffic conditions, resulting in suboptimal performance. Additionally, with fuel consumption emerging as a critical consideration alongside safety, there is a pressing need for more advanced solutions. This paper presents a novel approach to address these challenges by integrating Fuzzy ACC with Model Predictive Control, denoted as FACMPC. This integration aims to enhance both the longitudinal safety of AVs and fuel efficiency by considering real-time traffic conditions. The FACMPC system utilizes fuzzy logic inside the MPC, adaptively generates controller's weighting factors, allowing the system to adapt instantly to varying traffic environments and driving circumstances. The findings show that this adaptation improves the balance between driving safety, efficiency, and comfort. Additionally, three interruption scenarios, Alpha, Beta and Gama, are examined. In Alpha, the study evaluates the sensitivity of the FACMPC to disturbances by applying band-limited white noise to the lead vehicle velocity. In Beta, the AV experiences a loss of the lead vehicle velocity signal for a defined period, prompting safety considerations and assumptions. The Gama scenario includes a sensitivity analysis to account for variations and uncertainties in parameters by considering a range of ±5% around the nominal values for four key parameters: road slope, wind speed, wind direction, and rolling resistance. The findings indicate that the proposed controller's mean fuel consumption is 8.110, only a 3.21% increase over the nominal, compared to a 7.03% increase for the conventional ACC, demonstrating greater robustness against uncertainties.