Possibility Theory versus Probability Theory in Fuzzy Measure Theory

The purpose of this paper is to compare probability theory with possibility theory, and to use this comparison in comparing probability theory with fuzzy set theory. The best way of comparing probabilistic and possibilistic conceptualizations of uncertainty is to examine the two theories from a broader perspective. Such a perspective is offered by evidence theory, within which probability theory and possibility theory are recognized as special branches. While the various characteristic of possibility theory within the broader framework of evidence theory are expounded in this paper, we need to introduce their probabilistic counterparts to facilitate our discussion.