title: |
On the connection between probability boxes and possibility measures |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 836 - 843 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Matthias C. M. Troffaes, Enrique Miranda, Sebastien Destercke |
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publication date: |
July 2011 |
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keywords: |
Possibility measures, maxitive measures, pboxes, coherent upper previsions, natural extension. |
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abstract: |
We explore the relationship between p-boxes on totally
preordered spaces and possibility measures. We start by
demonstrating that only those p-boxes who have 0–1-
valued lower or upper cumulative distribution function
can be possibility measures, and we derive expressions
for their natural extension in this case. Next, we establish
necessary and sufficient conditions for a p-box to
be a possibility measure. Finally, we show that almost
every possibility measure can be modelled by a p-box.
Whence, any techniques for p-boxes can be readily applied
to possibility measures. We demonstrate this by
deriving joint possibility measures from marginals, under
varying assumptions of independence, using a technique
known for p-boxes. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |