Possibilistic information measure of importance in fault tree analysis

With respect to the subjective and nonlinear factors inherent in the importance identification of a fault tree analysis (FTA), a new importance measure of FTA is proposed based upon possibilistic information entropy. After investigating the possibilistic information semantics, measure-theoretic terms and entropy-like models, a two-dimensional framework is 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 an example of the fault tree is thus provided, along with the concordance analysis and otherness discussions. The more conservative numerical results of importance rankings which involved more choices could be viewed as “soft” fault identification under a certain expected value.