With respect to the subjective factors and nonlinear characteristics inherent in the important identifi-cation of fault tree analysis (FTA), a new important measure of FTA is proposed based on possibilistic information entropy. After investigating possibilistic information semantics, measure-theoretic terms, and entropy-like models, a two-dimensional framework has been constructed by combining both the set theory and the measure theory. By adopting the possibilistic assumption in place of the probabilistic one, an axiomatic index of importance is defined in the possibility space and then the modelling principles are presented. An example of the fault tree is thus provided, along with the concordance analysis and other discussions. The more conservative numerical results of importance rankings, which involve the more choices can be viewed as "soft" fault identification under a certain expected value. In the end, extension to evidence space and further research perspectives are discussed.
