This paper aims to find a good facility location under uncertain and vague circumstances by merging fuzzy set theory with strong optimization technologies. Traditional facility location models count on exact information, but real costs, demand levels, and capacity vary significantly. For this reason, a fuzzy mixed-integer programming model enables fuzzy numbers to represent these parameters. A new Genetic Algorithm (GA) is applied to work with the model efficiently, using α-cut transformations that let it address the fuzzy uncertainty before solving the different subproblems. Conducting computations on various test datasets proves that the algorithm creates solid and flexible facility location strategies in many uncertain situations. The results demonstrate that fuzziness leads to better and stronger solutions than classical approaches in strategic location decision-making. The suggested framework helps managers manage risks and costs well, boosting their operations even when uncertain.