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This paper computes the uncertainties associated with the power system state variables obtained with the help of phasor measurement units (PMUs). An integer-quadratic-programming-based method is used to determine the minimum number and the optimal locations of the PMUs to ensure complete topological observability of the system. Three approaches are used to estimate the uncertainties in the state variables: the use of the classical uncertainty propagation theory, the Monte Carlo method, and the random fuzzy variables (RFVs). The methods are applied on a test system, and the results are presented. The choice of method depends on the application; suggestions are offered based on the conclusions of the work in this paper.