On Possibility/Probability Transformations

Abstract

this paper that the probabilistic representations and the possibilistic ones are not just two equivalent representations of uncertainty. Hence there should be no symmetry between the two mutual conversion procedures. The possibilistic representation is weaker because it explicitly handles imprecision (e.g. incomplete knowledge) and because possibility measures are based on an ordering structure rather than an additive one. Turning a probability measure into a possibility measure may be useful in the presence of other weak sources of information, or when computing with possibilities is simpler than computing with probabilities. Turning a possibility measure into a probability measure might be of interest in the scope of decision-making (Smets, 1990). The next section suggests that the transformations should be guided by two different information principles : the principle of insufficient reason from possibility to probability, and the principle of maximum specificity from probability to possibility. The first principle aims at finding a probability measure which preserves the uncertainty of choice between outcomes, while the second principle aims at finding the most informative possibility distribution, under the constraints dictated by the possibility/probability consistency principle. The paper then proposes two transformations that obey these principles. In the discrete case they are already known. But here, results in the continuous case are given. It is pointed out that these transformations are not related to each other, and the converse transformations are shown to be inadequate. In the last section we discuss the relationship between our approach and other works pertaining to the same topic. Some lines of research are considered