The article provides the theoretical foundations of building a graph model of the survivability of a fuzzy network in terms of the theory of fuzzy sets of the second type. The possibility and the correctness of generalizing the concept of the fuzzy graph in terms of presentation of the set of n-ary relations for an arbitrary finite n ? ? have been studied. Definitions of the fuzzy hypergraph have been introduced. The natural spread of the concept of the degree of survivability on the hypergraph has been displayed. The main cases of reducing the survivability of the fuzzy oriented graph have been specified. Analyzes of the task of increasing the degree of survivability of a fuzzy transportation network by the criterion of least cost and its interpretation in the matters of air transportation have been carried out. The authors suggest a modification of the known algorithm that allows to increase the sum value of the functions of membership of the fuzzy graph edges so that its survivability can reach the desired value. It has been substantiated that, using the considered theoretical foundations, the proposed algorithm allows to enhance the degree of survivability of the fuzzy network of airports up to the specified level.