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Completely monotone outer approximations of lower probabilities on finite possibility spaces

Erik Quaeghebeur (UGent)
(2011) Advances in Intelligent and Soft Computing. 100. p.169-178
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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.
Keywords
outer approximation, lower probabilities, complete monotonicity, belief functions, Möbius transform

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MLA
Quaeghebeur, Erik. “Completely Monotone Outer Approximations of Lower Probabilities on FInite Possibility Spaces.” Advances in Intelligent and Soft Computing, edited by Shoumei Li et al., vol. 100, Springer, 2011, pp. 169–78, doi:10.1007/978-3-642-22833-9_20.
APA
Quaeghebeur, E. (2011). Completely monotone outer approximations of lower probabilities on finite possibility spaces. In S. Li, X. Wang, Y. Okazaki, J. Kawabe, T. Murofushi, & L. Guan (Eds.), Advances in Intelligent and Soft Computing (Vol. 100, pp. 169–178). https://doi.org/10.1007/978-3-642-22833-9_20
Chicago author-date
Quaeghebeur, Erik. 2011. “Completely Monotone Outer Approximations of Lower Probabilities on FInite Possibility Spaces.” In Advances in Intelligent and Soft Computing, edited by Shoumei Li, Xia Wang, Yoshiaki Okazaki, Jun Kawabe, Toshiaki Murofushi, and Li Guan, 100:169–78. Berlin, Germany: Springer. https://doi.org/10.1007/978-3-642-22833-9_20.
Chicago author-date (all authors)
Quaeghebeur, Erik. 2011. “Completely Monotone Outer Approximations of Lower Probabilities on FInite Possibility Spaces.” In Advances in Intelligent and Soft Computing, ed by. Shoumei Li, Xia Wang, Yoshiaki Okazaki, Jun Kawabe, Toshiaki Murofushi, and Li Guan, 100:169–178. Berlin, Germany: Springer. doi:10.1007/978-3-642-22833-9_20.
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.
IEEE
[1]
E. Quaeghebeur, “Completely monotone outer approximations of lower probabilities on finite possibility spaces,” in Advances in Intelligent and Soft Computing, Beijing, PR China, 2011, vol. 100, pp. 169–178.
@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 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       = {{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}},
  keywords     = {{outer approximation,lower probabilities,complete monotonicity,belief functions,Möbius transform}},
  language     = {{eng}},
  location     = {{Beijing, PR China}},
  pages        = {{169--178}},
  publisher    = {{Springer}},
  title        = {{Completely monotone outer approximations of lower probabilities on finite possibility spaces}},
  url          = {{http://doi.org/10.1007/978-3-642-22833-9_20}},
  volume       = {{100}},
  year         = {{2011}},
}
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