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This paper concentrates on sensitivity analysis of the fuzzy assignment problem (FAP). Since most real environments are uncertain, the FAP is more realistic than the assignment problem in application. Owing to the high degeneracy of the FAP, as that of the assignment problem, traditional sensitivity analysis, called Type I sensitivity analysis, which determines the range in which the current optimal basis remains optimal, is impractical. Hence, we attempt to perform other two types of advanced sensitivity analysis, called Type II and Type III sensitivity analysis, to overcome this problem. A labeling algorithm is then presented, where Type II sensitivity analysis is to determine the range of perturbation to keep the current optimal assignment remaining optimal, and Type III sensitivity analysis is to determine the range for which the rate of change of optimal value function remains unchanged. The procedure of the labeling algorithm is divided into two parts: one is when the unassigned cell is perturbed, and the other is when the assigned cell is perturbed. An example is presented to demonstrate that the labeling algorithm is a useful tool for determining the Type II and Type III sensitivity analysis of the FAP.