Fuzzy importance in fault tree analysis

In fault tree analysis, system success or failure can be described by the state of the top event, which is usually defined by a so-called structure function. In this paper, we attempt to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function, using fuzzy sets theory. Furthermore, it is shown that the importance of each basic event can be evaluated through fuzzy operations. The method proposed herein is demonstrated by some examples with respect to the failure analysis of structures.