The theory of fuzzy discrete event system (FDES) has been attracting increasing attention from the research community. To improve the ability of a FDES to handle complex uncertainties, the theory of extended fuzzy discrete event system (EFDES) was developed. However, any event in an EFDES is modeled by a FS only, so that an EFDES is insufficient to model an event and cannot model the evolution of the state variable well. To overcome this limitation, this paper presented the theory of generalized fuzzy discrete event system (GFDES). To establish the GFDES theory, the model of a GFDES was built first. Unlike an EFDES, any event in a GFDES is allowed to be characterized by its multiple attributes and each of its attributes can be represented by a FS. This representation of an event enables a GFDES to better model the evolution of the state variable. In addition, the complete procedure for implementing a GFDES including the steps of computing the current state vector, the fuzzy event transition matrix, the next state vector and the next state was presented.