An unified approach to the fusion of imperfect data?

For several years, researchers have explored the unification of the theories enabling the fusion of imperfect data and have finally considered two frameworks: the random sets and the conditional events algebra. Traditionally, the information is modeled and fused in one of the known theories: bayesian, fuzzy sets, possibilistic, evidential, or rough sets... Previous work has shown what kind of imperfect data these theories can best deal with. So, depending on the quality of the available information (uncertain, vague, imprecise,...), one particular theory seems to be the preferred choice for fusion. However, in a typical application, the variety of sources provides different kinds of imperfect data. The classical approach is then to model and fuse the incoming data in a single theory being previously chosen. In this paper, we first introduce the various kinds of imperfect data and then the theories that can be used to cope with the imperfection. We also present the existing relationships between them and detail the most important properties for each theory. We finally propose the random sets theory as a possible framework for unification, and thus show how the individual theories can fit in this framework.