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The theory of differential subordination was introduced by S.S. Miller and P.T. Mocanu in [1] and [2] then developed in many other papers. Using the notion of differential subordination, in [5] the authors define the notion of fuzzy subordination and in [6] they define the notion of fuzzy differential subordination.In this paper, we determine conditions for a function to be a dominant of the fuzzy differential subordination and we also give the best dominant.

Mathematics Subject Classification (2010): 30C20, 30C45, 30A20.

Keywords: Fuzzy set, fuzzy function, fuzzy subordination, fuzzy differential subordination, Briot-Bouquet fuzzy differential subordination, dominant, fuzzy best dominant.