Unifying practical uncertainty representations. II: Clouds

There exist many tools for capturing imprecision in probabilistic representations. Among them are random sets, possibility distributions, probability intervals, and the more recents Ferson’s p-boxes and Neumaier’s clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation can be turned into or approximated by other ones. In the companion paper, we have thoroughly studied a generalized form of p-box, relating it with other models. This paper focuses on so-called clouds and their links with other representations. In particular, it is shown that they are more general than generalized p-boxes and generally cannot be represented by convex capacities, hence by random sets.