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In this paper, fuzzy sets having the property of fuzzy Baire in the fuzzy topological spaces are introduced by means of fuzzy first category sets. The conditions for the existence of fuzzy Baireness and fuzzy resolvability of fuzzy topological spaces are established by means of fuzzy sets having the property of fuzzy Baire. It is established that there are no fuzzy sets having the property of fuzzy Baire in fuzzy hyperconnected spaces and fuzzy sets having the property of fuzzy Baire in fuzzy Baire spaces are fuzzy second category sets.