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Completely monotone outer approximations of lower probabilities on finite possibility spaces

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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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Please use this url to cite or link to this publication:

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.
@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},
}

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