Uncertainty Propagation Analysis of Fuzzy Uncertain Structures Involving Imprecise Membership Functions

Abstract

Uncertain structures may exhibit fuzzy uncertainty involving imprecise membership function (FuIMF). In this study, the uncertain parameters in FuIMF case are characterized as fuzzy variables, whereas the key parameters of their membership functions are treated as interval variables rather than exact values. Two ideas are put forward to handle FuIMF variables. First, the interval-boundary interval method (IBIM) is derived to conduct uncertainty propagation analysis, in which the [Formula: see text]-cut of FuIMF variables are considered as interval-boundary intervals. Second, the [Formula: see text]-cut of FuIMF variables are presented by the conservative and radical approximations, and the conservative and radical approximations method I (CRAM I) is proposed to conduct uncertainty propagation analysis. To further promote the computational efficiency, the conservative and radical approximations method II (CRAM II) is developed. Afterwards, a reference method based on Monte Carlo simulation is presented to verify the proposed methods. Finally, the effectiveness of proposed methods is demonstrated by numerical examples.