Unifying Practical Uncertainty Representations: II. Clouds

Abstract

There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models . This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by 2-monotone (convex) capacities.

30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expanded section concerning clouds and probability intervals)

References in corpus (1)

• Unifying Practical Uncertainty Representations: I. Generalized P-Boxes

Cited by in corpus (4)

• Uncertainty propagation of p-boxes using sparse polynomial chaos expansions
• Probability boxes on totally preordered spaces for multivariate modelling
• Computing Expectations with Continuous P-Boxes: Univariate Case
• Sherlock Holmes Doesn't Play Dice: The mathematics of uncertain reasoning when something may happen, that one is not even able to figure out