An imprecision importance measure for uncertainty representations interpreted as lower and upper probabilities, with special emphasis on possibility theory

Uncertainty importance measures typically reflect the degree to which uncertainty about risk and reliability parameters at the component level influences uncertainty about parameters at the system level. The definition of these measures is typically founded on a Bayesian perspective where subjective probabilities are used to express epistemic uncertainty; hence, they do not reflect the effect of imprecision in probability assignments, as captured by alternative uncertainty representation frameworks such as imprecise probability, possibility theory and evidence theory. In the present paper, we define an imprecision importance measure to evaluate the effect of removing imprecision to the extent that a probabilistic representation of uncertainty remains, as well as to the extent that no epistemic uncertainty remains. Possibility theory is highlighted throughout the paper as an example of an uncertainty representation reflecting imprecision, and used in particular in two numerical examples which are included for illustration.