Exploring importance analysis of fuzzy memberhship functions for structural system with mixed uncertain variables

Aim. The introduction of the full paper reviews a number of papers in the open literature and then proposes what we believe to be our new exploration, which is explained in section 1. The core of section 1 is: "For structural system models with both fuzzy uncertainties and random uncertainties, according to the idea of uncertainties from basic variables to the model output, and the difference between unconditional and conditional membership functions of the fuzzy reliability, new importance measures are defined to the reliability membership character diversification due to random variables and fuzzy variables respectively, and a stability index of the importance measure of random variables is defined subsequently. The defined importance measure is easy to apprehend, can save much computation time and has no restriction either to the distribution of random variables or the membership function of fuzzy variables, since all evaluation is based on the probability density function of basic random variables and the membership function of basic fuzzy variables, and the presented importance measures are global sensitivity indicators. " Section 2 applies the findings of our exploration to examples 1 and 2. The Monte Carlo simulation results for example 1 are presented in Table 1 and Fig. 3. For examples 2, we use the UUA (unified uncertainty analysis) method, which is based on the first order reliability method, to abtain the results: Table 3 and Fig. 4. The results of all examples and their analysis show preliminarly that our new exploration is promising but needs to be improved.