Notions of fuzzy internal stable and external stable sets of a fuzzy oriented graph and the degrees of the internal and external stability are defined. An approach to the determination of fuzzy internal stable and external stable sets with a maximal degree of stability is proposed. The approach is a generalization of the MAGU method for the discrimination of maximal internal and minimal external sets of an ordinary (not fuzzy) graph. The notion of a fuzzy kernel of a graph is also defined as the intersection of fuzzy internal and external sets and the degree of fuzziness of a graph. An approach to finding all fuzzy kernels of a graph with the maximal degree of fuzziness is considered.
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