In these last years, many arguments appeared, converging to the fact that classical probabilities cannot adequately handle or represent imprecision or incompleteness in the available information concerning a system, a variable or a parameter. Hence, alternative theories proposing to address and solve this issue have emerged. The three main such theories are, from the more to the less general: imprecise probability theory, random set theory, possibility theory.
With them also appeared new difficulties and questions related to the representation and treatment of uncertainty: difficulties regarding the practical handling of uncertainties, since explicitly modeling imprecision often means an higher computational complexity when treating the information; questions related to the interpretation of some notions (conditioning, independence) that almost met general consensus in classical probabilities; problems of unification due to the fact that uncertainty calculus and treatments are sometimes different between different theories and interpretations. Actually, by choosing a different or a more expressive framework to handle uncertainty, issues that were previously "hidden" by the somewhat restrictive setting of classical probability theory are no longer hidden in the new setting.
In this work, we bring some partial answers to above issues, first by trying to settle different problematics in unified settings, second by proposing practical methods allowing to handle uncertainty in an efficient way. We focus mainly on the following issue:
- The study of practical uncertainty representations. In particular, we situate more recent uncertainty representations (p-boxes and clouds) with respect to older uncertainty representations. This lead us to expose a number of interesting relations between representations, eventually leading to an easier practical handling of such representations.
- The combination of information coming from multiple sources. In particular, we look at the two problems of combining partially consistent information and of taking account of potential dependencies between information sources. We also address the issue of evaluating the quality of the delivered information by the use of past assessments
- Modeling and interpreting notions of independence between variables, these notions being essential in the construction of joint uncertainty models from marginal ones. Here, we simply gives a general picture of the (many) notions existing in the uncertainty theories
considered here, and propose some first results eventually leading to an unified frame. Indeed, a full study of the complex notion of independence would require a work of its own.
Finally, we briefly look at the problems of decision making, and give some details about two applications achieved during this work and using some of the methods exposed therein.