### Completely monotone outer approximations of lower probabilities on ﬁnite possibility spaces

Erik Quaeghebeur (2011) 100. p.169-178
abstract
Drawing inferences from general lower probabilities on finite possibility spaces usually involves solving linear programming problems. For some applications this may be too computationally demanding. Some special classes of lower probabilities allow for using computationally less demanding techniques. One such class is formed by the completely monotone lower probabilities, for which inferences can be drawn efficiently once their Möbius transform has been calculated. One option is therefore to draw approximate inferences by using a completely monotone approximation to a general lower probability; this must be an outer approximation to avoid drawing inferences that are not implied by the approximated lower probability. In this paper, we discuss existing and new algorithms for performing this approximation, discuss their relative strengths and weaknesses, and illustrate how each one works and performs.
author
organization
year
type
conference
publication status
published
subject
keyword
outer approximation, lower probabilities, complete monotonicity, belief functions, Möbius transform
in
Advances in Intelligent and Soft Computing
editor
Shoumei Li and Li Guan
volume
100
issue title
Nonlinear mathematics for uncertainty and its applications
pages
169 - 178
publisher
Springer
place of publication
Berlin, Germany
conference name
International conference on Nonlinear Mathematics for Uncertainty and its Applications
conference location
Beijing, PR China
conference start
2011-09-07
conference end
2011-09-09
ISSN
1867-5662
ISBN
9783642228339
9783642228322
DOI
10.1007/978-3-642-22833-9_20
language
English
UGent publication?
yes
classification
C1
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:339823
VABB type
VABB-5
id
1864309
handle
http://hdl.handle.net/1854/LU-1864309
date created
2011-08-01 15:37:37
date last changed
2017-01-02 09:53:15
```@inproceedings{1864309,
abstract     = {Drawing inferences from general lower probabilities on finite possibility spaces usually involves solving linear programming problems. For some applications this may be too computationally demanding. Some special classes of lower probabilities allow for using computationally less demanding techniques. One such class is formed by the completely monotone lower probabilities, for which inferences can be drawn efficiently once their M{\"o}bius transform has been calculated. One option is therefore to draw approximate inferences by using a completely monotone approximation to a general lower probability; this must be an outer approximation to avoid drawing inferences that are not implied by the approximated lower probability. In this paper, we discuss existing and new algorithms for performing this approximation, discuss their relative strengths and weaknesses, and illustrate how each one works and performs.},
author       = {Quaeghebeur, Erik},
booktitle    = {Advances in Intelligent and Soft Computing},
editor       = {Li, Shoumei and Wang, Xia and Okazaki, Yoshiaki and Kawabe, Jun and Murofushi, Toshiaki and Guan, Li},
isbn         = {9783642228339},
issn         = {1867-5662},
keyword      = {outer approximation,lower probabilities,complete monotonicity,belief functions,M{\"o}bius transform},
language     = {eng},
location     = {Beijing, PR China},
pages        = {169--178},
publisher    = {Springer},
title        = {Completely monotone outer approximations of lower probabilities on \unmatched{fb01}nite possibility spaces},
url          = {http://dx.doi.org/10.1007/978-3-642-22833-9\_20},
volume       = {100},
year         = {2011},
}

```
Chicago
Quaeghebeur, Erik. 2011. “Completely Monotone Outer Approximations of Lower Probabilities on Fnite Possibility Spaces.” In Advances in Intelligent and Soft Computing, ed. Shoumei Li, Xia Wang, Yoshiaki Okazaki, Jun Kawabe, Toshiaki Murofushi, and Li Guan, 100:169–178. Berlin, Germany: Springer.
APA
Quaeghebeur, E. (2011). Completely monotone outer approximations of lower probabilities on ﬁnite possibility spaces. In Shoumei Li, X. Wang, Y. Okazaki, J. Kawabe, T. Murofushi, & L. Guan (Eds.), Advances in Intelligent and Soft Computing (Vol. 100, pp. 169–178). Presented at the International conference on Nonlinear Mathematics for Uncertainty and its Applications, Berlin, Germany: Springer.
Vancouver
1.
Quaeghebeur E. Completely monotone outer approximations of lower probabilities on ﬁnite possibility spaces. In: Li S, Wang X, Okazaki Y, Kawabe J, Murofushi T, Guan L, editors. Advances in Intelligent and Soft Computing. Berlin, Germany: Springer; 2011. p. 169–78.
MLA
Quaeghebeur, Erik. “Completely Monotone Outer Approximations of Lower Probabilities on Fnite Possibility Spaces.” Advances in Intelligent and Soft Computing. Ed. Shoumei Li et al. Vol. 100. Berlin, Germany: Springer, 2011. 169–178. Print.