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

P.-E. Doré; A. Martin; I. Abi-Zeid; A.-L. Jousselme; P. Maupin

RAIRO - Operations Research - Recherche Opérationnelle (2010)

  • Volume: 44, Issue: 4, page 323-343
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Doré, P.-E., et al. "Belief functions induced by multimodal probability density functions, an application to the search and rescue problem." RAIRO - Operations Research - Recherche Opérationnelle 44.4 (2010): 323-343. <http://eudml.org/doc/245966>.

@article{Doré2010,
abstract = {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.},
author = {Doré, P.-E., Martin, A., Abi-Zeid, I., Jousselme, A.-L., Maupin, P.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {continuous belief function; multimodal probability density function; consonant belief function; optimal search; search and rescue (SAR)},
language = {eng},
number = {4},
pages = {323-343},
publisher = {EDP-Sciences},
title = {Belief functions induced by multimodal probability density functions, an application to the search and rescue problem},
url = {http://eudml.org/doc/245966},
volume = {44},
year = {2010},
}

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
PB - EDP-Sciences
VL - 44
IS - 4
SP - 323
EP - 343
AB - 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.
LA - eng
KW - continuous belief function; multimodal probability density function; consonant belief function; optimal search; search and rescue (SAR)
UR - http://eudml.org/doc/245966
ER -

References

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