Possibility theory vs. probability theory in decision analysis

In decision analysis, information analysis, reliability theory, control theory, choice theory, game theory and most other theories in which the concept of uncertainty plays an important role, it has long been -- and continues to be -- an unquestion assumption that uncertainty is a concomitant of randomness and, as such, should be treated by the methods provided by probability theory. However, as we learn more about the issues relating to uncertainty, it is becoming increasingly clear that randomness and uncertainty are by no means coextensive concepts, and that uncertainty has two distinct facets -- fuzziness and randomness -- both of which play basic roles in human reasoning, decision-making and concept formation.