Post - processing the hybrid method for addressing uncertainty in risk assessments

In this journal, a “hybrid method” was proposed for the joint propagation of probability distributions (expressing variability) and possibility distributions (i.e., fuzzy numbers, expressing imprecision or partial ignorance) in the computation of risk. In order to compare the results of the hybrid computation (a random fuzzy set) to a tolerance threshold (a tolerable level of risk), a post-processing method was proposed. Recent work has highlighted a shortcoming of this post-processing step which yields overly-conservative results. A post-processing method based on Shafer’s theory of evidence provides a rigorous answer to the problem of comparing a random fuzzy set with a threshold. The principles behind the new post-processing scheme are presented and illustrated with a synthetic example.