In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two examples of probability density functions (unimodal and multimodal). On a case study of Search And Rescue (SAR), we extend the traditional probabilistic framework of search theory to continuous belief functions theory. We propose a new optimization criterion to allocate the search effort as well as a new rule to update the information about the lost object location in this latter framework. We finally compare the allocation of the search effort using this alternative uncertainty representation to the traditional probabilistic representation.

Keywords: continuous belief function, multimodal probability density function, consonant belief function, optimal search, search and rescue (SAR)

@article{RO_2010__44_4_323_0, author = {Dor\'e, P.-E. and Martin, A. and Abi-Zeid, I. and Jousselme, A.-L. and Maupin, P.}, title = {Belief functions induced by multimodal probability density functions, an application to the search and rescue problem}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {323--343}, publisher = {EDP-Sciences}, volume = {44}, number = {4}, year = {2010}, doi = {10.1051/ro/2011001}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2011001/} }

TY - JOUR AU - Doré, P.-E. AU - Martin, A. AU - Abi-Zeid, I. AU - Jousselme, A.-L. AU - Maupin, P. TI - Belief functions induced by multimodal probability density functions, an application to the search and rescue problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2010 SP - 323 EP - 343 VL - 44 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2011001/ DO - 10.1051/ro/2011001 LA - en ID - RO_2010__44_4_323_0 ER -

%0 Journal Article %A Doré, P.-E. %A Martin, A. %A Abi-Zeid, I. %A Jousselme, A.-L. %A Maupin, P. %T Belief functions induced by multimodal probability density functions, an application to the search and rescue problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2010 %P 323-343 %V 44 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2011001/ %R 10.1051/ro/2011001 %G en %F RO_2010__44_4_323_0

Doré, P.-E.; Martin, A.; Abi-Zeid, I.; Jousselme, A.-L.; Maupin, P. Belief functions induced by multimodal probability density functions, an application to the search and rescue problem. RAIRO - Operations Research - Recherche Opérationnelle, Volume 44 (2010) no. 4, pp. 323-343. doi : 10.1051/ro/2011001. http://archive.numdam.org/articles/10.1051/ro/2011001/

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