Abstract: In order to overcome the uncertainties of components failure probabilities and fault states and fault mechanisms in fault tree analysis, the components failure possibilities are denoted by fuzzy subsets, the fault states of components and system are expressed as fuzzy numbers, the components’ relations are described by T-S fuzzy model. On the basis of T-S fuzzy fault tree analysis method, two kinds of T-S fuzzy importance algorithms are proposed: Combining with the influence of all fault states’ failure possibilities of components on the importance degree of system, the T-S fuzzy importance of multi-state system is defined by extending the centroid method of the conventional two-state system fuzzy importance, it is showed that the conventional fuzzy importance can be regarded as a special example of the T-S fuzzy importance and the proposed algorithm is more general; Under the condition of only knowing components fault states, the concept and calculation method of T-S state importance are presented. It is proved that the algorithms are feasible by importance analysis of a certain navigation system.

Key words: Fault tree, Fuzzy subset, Importance, Multi-state system, T-S fuzzy