A general framework for comparing numerical uncertainty theories

Deciding which of the existing uncertainty theories is the appropriate one to use in the formalization of a given problem is still a difficult task. It is possible to compare these theories either using pragmatic considerations (e.g. efficiency) or experimentally applying them on a set of problems; however, up to now there is no general frame in which we can compare the uncertainty theories with respect to their meanings. Our work aims to develop a general formalism for representing and reasoning with uncertain knowledge, which provides such a framework and is not restricted in using one specific uncertainty theory as a basis. This formalism is based on the work of Carnap´s logical foundation of probability. But, instead of propositions, we regard distinctions as elementary notions. Up until now, the following theories can be expressed within the framework: Bayes theory, fuzzy set theory, Dempster/Shafer theory (belief functions) and upper/lower probability theory