Introduction

A standard example that points out the difference between degrees of uncertainty and degrees of truth is that of a bottle. In terms of binary truth values, a bottle is viewed as full or empty. Note that all vague/fuzzy statements are truth-functional, that is, the degree of truth of every statement can be calculated from the degrees of truth of its constituents, while uncertain statements cannot be a function of the uncertainties of their constituents. Intuitively, the probability of an event aggregates the probabilities of all worlds that satisfy this event, whereas the possibility of an event is simply the possibility of the “most optimistic” world that satisfies the event. Hence, although both probability and possibility theory allow for quantifying degrees of uncertainty, they are conceptually quite.