Possibility Theory: Qualitative and Quantitative Aspects

TLDR: Possibility theory offers a simple, non-additive modelling of partial belief, which contrasts with probability theory, and provides a potentially more qualitative treatment ofpartial belief since the operations ‘max’ and ‘min’ play a role somewhat analogous to the sum and the product in probability calculus.

Abstract: In recent years there has been a major trend in uncertainty (more specifically, partial belief) modelling emphasizing the idea that the degree of confidence in an event is not totally determined by the confidence in the opposite event, as assumed in probability theory. Possibility theory belongs to this trend that describes partial belief in terms of certainty and plausibility, viewed as distinct concepts. The distinctive features of possibility theory are its computational simplicity, and its position as a bridge between numerical and symbolic theories of partial belief for practical reasoning. The name ‘possibility theory’ was coined by L. A. Zadeh in the late seventies [Zadeh, 1978a] as an approach to uncertainty induced by pieces of vague linguistic information, described by means of fuzzy sets [Zadeh, 1965]. Possibility theory offers a simple, non-additive modelling of partial belief, which contrasts with probability theory. As we shall see, it provides a potentially more qualitative treatment of partial belief since the operations ‘max’ and ‘min’ play a role somewhat analogous to the sum and the product in probability calculus.