A generalized Borgonovoʹs importance measure for fuzzy input uncertainty

In this work, the way in which fuzzy uncertainty in a modelʹs output is apportioned to fuzzy uncertainty in model inputs is studied through a sensitivity analysis. Here, an optimization technique is employed to obtain the membership functions of the fuzzy structural response, for which a global sensitivity indicator is introduced to measure the influence of fuzzy input uncertainty on fuzzy output uncertainty. The global sensitivity indicator is the important measure of the fuzzy input uncertainty, which extends Borgonovoʹs measure. In this study, the mathematical properties of the important measure of the fuzzy input uncertainty are discussed and proved. The results of numerical examples and engineering examples show that the proposed importance measure can effectively describe the effect of fuzzy input uncertainty on fuzzy structural response. When the sensitivity indicator is larger, the basic fuzzy-valued variable becomes more important. The sensitivity indicators of the fuzzy structural response can give an essential importance sequence of all the basic fuzzy-valued variables and identify key contributing fuzzy-valued variables. The sensitivity indicators can provide the availability guidance to reduce the number of basic variables and optimize the fuzzy response model.