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Natural Extension of Choice Functions

Arthur Van Camp (UGent), Enrique Miranda (UGent) and Gert De Cooman (UGent)
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Abstract
We extend the notion of natural extension, that gives the least committal extension of a given assessment, from the theory of sets of desirable gambles to that of choice functions. We give an expression of this natural extension and characterise its existence by means of a property called avoiding complete rejection. We prove that our notion reduces indeed to the standard one in the case of choice functions determined by binary comparisons, and that these are not general enough to determine all coherent choice function. Finally, we investigate the compatibility of the notion of natural extension with the structural assessment of indifference between a set of options.
Keywords
Choice functions, Coherence, Natural extension, Sets of desirable gambles, Structural assessments.

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Citation

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Chicago
Van Camp, Arthur, Enrique Miranda, and Gert De Cooman. 2018. “Natural Extension of Choice Functions.” In , ed. Jesús Medina, Manuel Ojeda-Aciego, José Luis Verdegay, David Pelta, Inma Cabrera, Bernadette Bouchon-Meunier, and Ronald Yager, 854:201–213. Springer International Publishing.
APA
Van Camp, Arthur, Miranda, E., & De Cooman, G. (2018). Natural Extension of Choice Functions. In J. Medina, M. Ojeda-Aciego, J. Luis Verdegay, D. Pelta, I. Cabrera, B. Bouchon-Meunier, & R. Yager (Eds.), (Vol. 854, pp. 201–213). Presented at the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Springer International Publishing.
Vancouver
1.
Van Camp A, Miranda E, De Cooman G. Natural Extension of Choice Functions. In: Medina J, Ojeda-Aciego M, Luis Verdegay J, Pelta D, Cabrera I, Bouchon-Meunier B, et al., editors. Springer International Publishing; 2018. p. 201–13.
MLA
Van Camp, Arthur, Enrique Miranda, and Gert De Cooman. “Natural Extension of Choice Functions.” Ed. Jesús Medina et al. Vol. 854. Springer International Publishing, 2018. 201–213. Print.
@inproceedings{8570710,
  abstract     = {We extend the notion of natural extension, that gives the least committal extension of a given assessment, from the theory of sets of desirable gambles to that of choice functions. We give an expression of this natural extension and characterise its existence by means of a property called avoiding complete rejection. We prove that our notion reduces indeed to the standard one in the case of choice functions determined by binary comparisons, and that these are not general enough to determine all coherent choice function. Finally, we investigate the compatibility of the notion of natural extension with the structural assessment of indifference between a set of options.},
  author       = {Van Camp, Arthur and Miranda, Enrique and De Cooman, Gert},
  editor       = {Medina, Jes{\'u}s and Ojeda-Aciego, Manuel and Luis Verdegay, Jose\unmatched{0301} and Pelta, David and Cabrera, Inma and Bouchon-Meunier, Bernadette and Yager, Ronald},
  isbn         = {9783319914756},
  issn         = {1865-0929},
  keyword      = {Choice functions,Coherence,Natural extension,Sets of desirable gambles,Structural assessments.},
  language     = {eng},
  location     = {C{\'a}diz, Spain},
  pages        = {201--213},
  publisher    = {Springer International Publishing},
  title        = {Natural Extension of Choice Functions},
  url          = {http://dx.doi.org/10.1007/978-3-319-91476-3\_17},
  volume       = {854},
  year         = {2018},
}

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