Importance Measure for Fuzzy Structural Systems from the Probabilistic Perspective and Its Solving Algorithms

To effectively determine the influences of fuzzy uncertainties on structural systems in engineering, according to the fuzzy failure probability (FFP) model, which is based on the probabilistic perspective, the importance measure (IM) technique is extended to fuzzy uncertain structural systems. A novel IM framework, i.e., the fuzzy-failure-probability-based IM (FFP-IM), is established. By transforming the fuzzy failure probability into the expected value of the function for the failure domain, the proposed FFP-IM index can be represented as the variance-based IM of that index function. Then, an efficient solution algorithm for the proposed FFP-IM index is established based on the state-dependent parameter method. Ultimately, the Ishigami function, alongside three practical engineering examples, validates the proposed FFP-IM’s rationality and applicability. Furthermore, these examples illustrate the solution algorithm’s superior computational efficiency and accuracy.