Fuzzy label methods for constructing imprecise limit state functions

Abstract

In reliability analysis of engineering systems it is conventional to represent the limit state function as a precise surface. Uncertainty in the limit state function may be represented by introducing one or more additional random variables. However, the meaning of the additional random variable(s) is unclear and seldom does justice to the uncertainties in the subtle combination of expert judgement and sometimes scarce data from which the limit state function is constructed. Two new methods based on linguistic covering of the state space with fuzzy labels are introduced and used to generate an imprecise limit state function from very scarce experimental data. An example from flood defence engineering is used to demonstrate how plausible relaxations of the strong assumptions in the conventional probabilistic approach can generate wide bounds on the probability of system failure.