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Compared with a binary system model, a multi-state system model provides a more flexible tool for representing engineering systems in real life. In conventional multi-state theory, it is assumed that the exact probability and performance level of each component state are given. However, it may be difficult to obtain sufficient data to estimate the precise values of these probabilities and performance levels in many highly reliable modern engineering systems. New techniques are needed to solve these fundamental problems. A general fuzzy multi-state system model is proposed in this article to overcome these deficiencies. The basic definitions and assumptions of such systems are introduced. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Future research directions include performance evaluation algorithms for the defined fuzzy multi-state systems.