Joint Propagation and Exploitation of Probabilistic and Possibilistic Information in Risk Assessment

TLDR

Risk assessment uncertainty comprises random variability, modeled by probability distributions, and imprecision, better captured by possibility distributions. The study proposes a hybrid method to jointly propagate probabilistic and possibilistic uncertainty, summarize the resulting random fuzzy intervals, and evaluate tolerance threshold violations. The hybrid approach jointly propagates probabilistic and possibilistic uncertainty using evidence theory, demonstrates the method on synthetic examples, and corrects overly conservative exploitation procedures. The method yields random fuzzy interval outputs and, compared to previous exploitation procedures, produces less conservative results.

Abstract

Random variability and imprecision are two distinct facets of the uncertainty affecting parameters that influence the assessment of risk. While random variability can be represented by probability distribution functions, imprecision (or partial ignorance) is better accounted for by possibility distributions (or families of probability distributions). Because practical situations of risk computation often involve both types of uncertainty, methods are needed to combine these two modes of uncertainty representation in the propagation step. A hybrid method is presented here, which jointly propagates probabilistic and possibilistic uncertainty. It produces results in the form of a random fuzzy interval. This paper focuses on how to properly summarize this kind of information; and how to address questions pertaining to the potential violation of some tolerance threshold. While exploitation procedures proposed previously entertain a confusion between variability and imprecision, thus yielding overly conservative results, a new approach is proposed, based on the theory of evidence, and is illustrated using synthetic examples.