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In this paper, a QoS unicast routing problem is solved by means of a generalized fuzzy-constrained model. Both imprecision of the IP network state information and the fuzziness of QoS constraints are taken into account invoking fuzzy set theory. We have developed an algorithm, which is based on the classic Ford-Moore-Bellman algorithm, whose outcome is a fuzzy set of non-dominated paths. Its effectiveness is verified by comparison with results of a known crisp model.