Uncertainties in the analysis and design parameters of a gravity dam are spread out over the system and make the stability safety factors uncertain too. To analyze the effects of such uncertainties on the dam performance, a conceptual model based on the fuzzy sets theory is introduced here. The input uncertainties are simulated by triangular fuzzy numbers and introduced to the governing equations. To evaluate the extreme values of the dam safety factors, a many objective optimization problem is formed. To solve the problem efficiently, a many-objective genetic algorithm (MOGA) is coupled to the dam stability analysis model. The model is able to estimate all extreme values of the dam safety factors in only one single optimization run. An example gravity dam with and without uncertainty is analyzed respectively by the traditional and the fuzzy approaches. It is found that small input uncertainties can highly influence the analysis responses and, the proposed method can efficiently capture all safety factors uncertainties. For example, the simulations revealed that only +/- 10% uncertainty in the dam design parameters would lead to about -346 to +146 % uncertainty in the stability safety factors.