On the connection between probability boxes and possibility measures

DOI

10.2991/eusflat.2011.150How to use a DOI?

Keywords

Possibility measures, maxitive measures, pboxes, coherent upper previsions, natural extension.

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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Matthias C. M. Troffaes
AU  - Enrique Miranda
AU  - Sebastien Destercke
PY  - 2011/08
DA  - 2011/08
TI  - On the connection between probability boxes and possibility measures
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 836
EP  - 843
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.150
DO  - 10.2991/eusflat.2011.150
ID  - Troffaes2011/08
ER  -