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In this paper, we introduce the concept of relative fuzzy annihilator ideals in C-algebras and investigate some its properties. We characterize relative fuzzy annihilators in terms of fuzzy points. It is proved that the class of fuzzy ideals of C-algebras forms Heything algebra. We observe that the class of all fuzzy annihilator ideals can be made as a complete Boolean algebra. Moreover, we study the concept of fuzzy annihilator preserving homomorphism. We provide a sufficient condition for a homomorphism to be a fuzzy annihilator preserving.