Abstract
In conventional probability-based fault-tree analysis, the vague property in many systems, especially, the man-machine system is often ignored. To overcome this disadvantage, the fuzzy set theory is applied to fault-tree analysis. The failure possibility defined by a triangular fuzzy number on the interval [0,1] is used to characterize the possible deviation of the basic events. The fuzzy operations according to the extension principle is used to calculate the failure possibility of the top event. Furthermore, a fuzzy importance index is proposed to demonstrate the contribution of a basic event to the safety improvement of the top event in a fuzzy environment. © 1993.