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After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to H_v-modules. The notion of an intuitionistic fuzzy H_v-submodule of an H_v-module is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy H_v-submodules are given.