# 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 (2011)

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

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topDoré, P.-E., et al. "Belief functions induced by multimodal probability density functions, an application to the search and rescue problem." RAIRO - Operations Research 44.4 (2011): 323-343. <http://eudml.org/doc/44708>.

@article{Doré2011,

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},

keywords = {Continuous belief function; multimodal probability density function;
consonant belief function; optimal search; search and rescue (SAR); continuous belief function; consonant belief function},

language = {eng},

month = {1},

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/44708},

volume = {44},

year = {2011},

}

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

DA - 2011/1//

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); continuous belief function; consonant belief function

UR - http://eudml.org/doc/44708

ER -

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