The importance measure of fuzzy input on failure credibility under the fuzzy uncertainty

Since failure credibility has some perfect properties such as the self-duality, it is developed to be a popular failure measure indicator under the fuzzy uncertainty. In order to globally measure the contribution of fuzzy input to the failure credibility, the failure-credibility-based importance measure (FC-IM) is proposed in this paper. It is defined by the fuzzy average difference between unconditional failure credibility and conditional one on fixing the fuzzy input over its entire fuzzy input distribution range, and the mathematical properties of the proposed FC-IM are also discussed. Additionally, an efficient method by combining adaptive Kriging and double-loop fuzzy simulation is developed to estimate FC-IM. Finally, three examples are presented to illustrate the rationality of the proposed FC-IM and the feasibility of the proposed estimation method for FC-IM.