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Abstract
We study n-monotone lower previsions, which constitute a generalisation of n-monotone lower probabilities. We investigate their relation with the concepts of coherence and natural extension in the behavioural theory of imprecise probabilities, and improve along the way upon a number of results from the literature. Finally, we indicate how many approaches to integration in the literature fall squarely within the framework of the present study of coherent n-monotone lower previsions. This discussion allows us to characterise which types of integrals can be used to calculate the natural extension of a probability charge.
Keywords
n-monotonicity, comonotone additivity, Choquet integral, coherence, natural extension, PROBABILITIES, lower integral, lower prevision

Citation

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MLA
De Cooman, Gert, Matthias Troffaes, and Enrique Miranda. “n-Monotone Lower Previsions and Lower Integrals.” ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS. Ed. FG Cozman, R Nau, & T Seidenfeld. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA), 2005. 145–154. Print.
APA
De Cooman, Gert, Troffaes, M., & Miranda, E. (2005). n-Monotone lower previsions and lower integrals. In FG Cozman, R. Nau, & T. Seidenfeld (Eds.), ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS (pp. 145–154). Presented at the 4th International Symposium on Imprecise Probabilities and Their Applications, Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Chicago author-date
De Cooman, Gert, Matthias Troffaes, and Enrique Miranda. 2005. “n-Monotone Lower Previsions and Lower Integrals.” In ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, ed. FG Cozman, R Nau, and T Seidenfeld, 145–154. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Chicago author-date (all authors)
De Cooman, Gert, Matthias Troffaes, and Enrique Miranda. 2005. “n-Monotone Lower Previsions and Lower Integrals.” In ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, ed. FG Cozman, R Nau, and T Seidenfeld, 145–154. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Vancouver
1.
De Cooman G, Troffaes M, Miranda E. n-Monotone lower previsions and lower integrals. In: Cozman F, Nau R, Seidenfeld T, editors. ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA); 2005. p. 145–54.
IEEE
[1]
G. De Cooman, M. Troffaes, and E. Miranda, “n-Monotone lower previsions and lower integrals,” in ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, Pittsburgh, PA, USA, 2005, pp. 145–154.
@inproceedings{327210,
  abstract     = {We study n-monotone lower previsions, which constitute a generalisation of n-monotone lower probabilities. We investigate their relation with the concepts of coherence and natural extension in the behavioural theory of imprecise probabilities, and improve along the way upon a number of results from the literature. Finally, we indicate how many approaches to integration in the literature fall squarely within the framework of the present study of coherent n-monotone lower previsions. This discussion allows us to characterise which types of integrals can be used to calculate the natural extension of a probability charge.},
  author       = {De Cooman, Gert and Troffaes, Matthias and Miranda, Enrique},
  booktitle    = {ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS},
  editor       = {Cozman, FG and Nau, R and Seidenfeld, T},
  keywords     = {n-monotonicity,comonotone additivity,Choquet integral,coherence,natural extension,PROBABILITIES,lower integral,lower prevision},
  language     = {eng},
  location     = {Pittsburgh, PA, USA},
  pages        = {145--154},
  publisher    = {International Society for Imprecise Probability: Theories and Applications (SIPTA)},
  title        = {n-Monotone lower previsions and lower integrals},
  year         = {2005},
}

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