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Belief functions induced by multimodalprobability density functions,an application to the search and rescue problem

Published online by Cambridge University Press:  11 January 2011

P.-E. Doré ,
A. Martin ,
I. Abi-Zeid ,
A.-L. Jousselme  and
P. Maupin
P.-E. Doré
Affiliation:
E3I2-EA3876/ENSTA, 2 rue François Verny, 29806 Brest Cedex 09, France. [email protected]
A. Martin
Affiliation:
E3I2-EA3876/ENSTA, 2 rue François Verny, 29806 Brest Cedex 09, France. [email protected]
I. Abi-Zeid
Affiliation:
CERMID - Dpt. OSD, FSA - Université Laval, Québec, QC, G1K 7P4, Canada.
A.-L. Jousselme
Affiliation:
Defense R&D Canada-Valcartier, 2459 Pie-XI, Blvd North, QC, G3J 1X5, Canada.
P. Maupin
Affiliation:
Defense R&D Canada-Valcartier, 2459 Pie-XI, Blvd North, QC, G3J 1X5, Canada.
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Abstract

In this paper, we propose a new method to generate a continuousbelief functions from a multimodal probability distribution function definedover a continuous domain. We generalize Smets' approach in the sense thatfocal elements of the resulting continuous belief function can be disjoint setsof the extended real space of dimension n. We then derive the continuousbelief function from multimodal probability density functions using the leastcommitment principle. We illustrate the approach on two examples of probabilitydensity functions (unimodal and multimodal). On a case study of Search AndRescue (SAR), we extend the traditional probabilistic framework of search theoryto continuous belief functions theory. We propose a new optimization criterionto allocate the search effort as well as a new rule to update the informationabout the lost object location in this latter framework. We finally compare theallocation of the search effort using this alternative uncertaintyrepresentation to the traditional probabilistic representation.

Keywords

Continuous belief functionmultimodal probability density functionconsonant belief functionoptimal searchsearch and rescue (SAR)
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 4: COGIS'09 , October 2010 , pp. 323 - 343
Copyright
© EDP Sciences, ROADEF, SMAI, 2011

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