Possibilistic Evidence

PRico003International audienceThe paper investigates a qualitative counterpart of Shafer’s evidence theory, where the basic probability assignment is turned into a basic possibility assignment whose weights have 1 as a maximum. The associated set functions, playing the role of belief, plausibility, commonality, and the dual of the latter, are now defined on a “maxitive”, rather than on an additive basis. Although this possibilistic evidence setting has been suggested for a long time, and has a clear relation with the study of qualitative M¿obius transforms, it has not been really systematically studied and considered for itself as a general qualitative representation framework. It can be viewed as defining imprecise possibilities, and encompasses standard possibilitistic representations as a particular case. The paper particularly focuses on a generalized set-theoretic view of this setting and discusses the entailment relation between basic possibility assignments as well as combination rules