Assessing probability and possibility of catastrophic failure in managed systems using sparse fuzzy data

Comparing risks of rare, high consequence events poses serious challenges to social decision making as well as deep methodological and epistemological problems. It is necessary to assess the merits of countermeasures that are only useful in extremely unlikely circumstances. The value of a conventional conditional probability P(A|B)=P(A∩B)/P(B) becomes too uncertain to be useful when P(B) is not well measurably different from zero. Possibility theory offers a solution to this dilemma. This paper presents a mathematical model of possibilistic uncertainty in the context of "adventitious" events for which the uncertainty surrounding the best estimate of the rate of occurrence is larger than that best estimate itself.