Lu et al. [27] de_ned derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the de_nitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the de_nitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.