Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods

5

Evidence Theory for Treating Uncertainty

Evidence theory, also known as Dempster–Shafer theory or as the theory of belief functions, was established by Shafer (1976) for representing and reasoning with uncertain, imprecise, and incomplete information (Smets, 1994). It is a generalization of the Bayesian theory of subjective probability in the sense that it does not require probabilities for each event of interest, but bases belief in the truth of an event on the probabilities of other propositions or events related to it (Shafer, 1976). Evidence theory provides an alternative to the traditional manner in which probability theory is used to represent uncertainty by means of the specification of two degrees of likelihood, belief and plausibility, for each event under consideration. Evidence theory is introduced here with reference to Example 5.1, assuming that we have available knowledge in a different format than that considered in Chapters 3 and 4. The presentation in this chapter is in part taken from or based on Flage et al. (2009).

Example 5.1

With respect to the occurrence of a scenario of critical or catastrophic class, we assume we have available the same expert statement as considered in Chapter 3: that is, the probability of occurrence of a catastrophic class (CA) scenario (i.e., is greater than 0.2, and the probability of occurrence of a scenario of catastrophic (CA) ...