In water-supply pipe networks, inherent uncertainties in the analysis parameters, including nodal demands, pipe friction factors, reservoir heads, etc., lead to imprecise hydraulic responses. This study introduces a methodology based on fuzzy set theory to analyze network hydraulics under uncertainty. The fuzzy approach results in a complex optimization problem that is neither single nor common multiobjective. To solve the problem efficiently to find extreme values of nodal pressures and pipe velocities, a novel many-objective particle swarm optimization (MO-PSO) model is developed and coupled to a network hydraulic simulation model from the literature. The coupled model is applied against a benchmark example and a real pipe network from the literature and the results are compared with those from the previous methods. The examples manifest that the proposed fuzzy MO-PSO is computationally efficient and reliable. Analyzing the real pipe network shows that, for instance, +/- 15% uncertainty in the pipes' roughness and nodal demands could averagely result in -11.2 to +6.4% uncertainty in the nodal pressures and -41.7 to +50.1% in the pipe velocities.