Aiming at the problem that the existing fault diagnosis method has too high requirements for systems, the weak diagnosability of fuzzy discrete event system (FDES) is studied, and a weak fuzzy diagnosability method is proposed, which extends the weak diagnosability method of classical discrete event system (DES) to the fuzzy system. Firstly, the notion of weak fuzzy diagnosability of FDES is formalized; In order to verify the weak fuzzy diagnosability of fuzzy systems, a verifier automaton is constructed, and the necessary and sufficient conditions for the weak fuzzy diagnosability of FDES are obtained, in which the weak fuzzy fault diagnosis of fuzzy systems is realized. This method is suitable for weak fault diagnosis of both FDES and classical DES.