This paper gives a decentralized approach to the problem of failure prognosis in the framework of fuzzy discrete event systems (FDES). A notion of co-predictability is formalized for decentralized prognosis of FDESs, where several local agents with fuzzy observability rather than crisp observability are used in the prognosis task. An FDES is said to be co-predictable if each faulty event can be predicted prior to its occurrence by at least one local agent using the observability of fuzzy events. The verification of the decentralized predictability is performed by constructing a fuzzy co-verifier from a given FDES. The complexity of the fuzzy co-verifier is polynomial with respect to the FDES being predicted, and is exponential with respect to the number of the local prognosis agents. Then, a necessary and sufficient condition for the co-predictability of FDESs is given. In addition, we show that the proposed method may be used to deal with the decentralized prognosis for both FDESs and crisp DESs. Finally, to illustrate the effectiveness of the approach, some examples are provided.