The Formal Analogy between Possibility and Probability Theory

It is well known that the theory of probability can be treated and developed in a consistent and uniform way using the classical theory of measure and integration. Indeed, the Russian scientist Kolmogorov identified probability with normalized classical measures and used the Lebesgue theory of integration to give a logically consistent and unifying account of probability theory. In this paper, we indicate how, in an analogous way, a unified and consistent treatment of possibility theory can be given. Using seminormed fuzzy integrals, a generalization of Sugeno’s fuzzy integrals ideally suited for working with our possibility measures, we discuss how a theory of possibility can be developed along the same formal lines as the theory of probability.