Unifying Practical Uncertainty Representations: II. Clouds

Details Unifying Practical Uncertainty Representations: II. Clouds Unifying Practical Uncertainty Representations: II. Clouds

2008-08-20

arxiv.org/abs/0808.2779v1

Mathematics

Probability

30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expand

Scientific paper

10.1016/j.ijar.2008.07.004

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.

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