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. © 2011. The authors-Published by Atlantis Press.
CITATION STYLE
Troffae, M. C. M., Miranda, E., & Destercke, S. (2011). On the connection between probability boxes and possibility measures. In Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2011 and French Days on Fuzzy Logic and Applications, LFA 2011 (Vol. 1, pp. 836–843). https://doi.org/10.2991/eusflat.2011.150
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