Unifying Practical Uncertainty Representations: I. Generalized P-Boxes

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

2008-08-20

arxiv.org/abs/0808.2747v1

Mathematics

Probability

29 pages, 6 figures, pre-print of the final journal paper to be published in International Journal of Approximate Reasoning (I

Scientific paper

10.1016/j.ijar.2008.07.003

There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study.

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