Advertisement

A Formal language for convex sets of probabilities

  • Serafín Moral
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)

Abstract

In this paper, a new language for convex sets of probabilities operators is presented. Its main advantage is that it allows a more direct representation of initial pieces of information without transforming them in more complex representations. The language includes logical operators and numerical values. It will allow, in some cases, a reduction of the complexity of the calculations associated to convex sets of probabilities.

Keywords

Convex Hull Extreme Point Formal Language Imprecise Probability Conditional Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cano J.E., M. Delgado, S. Moral (1993) An axiomatic system for the propagation of uncertainty in directed acyclic networks. International Journal of Approximate Reasoning 8, 253–280.Google Scholar
  2. 2.
    Cano J.E., S. Moral, J.F. Verdegay-López (1991) Combination of Upper and Lower Probabilities. In: Uncertainty in Artificial Intelligence. Proceedings of the 7th Conference (B.D'Ambrosio, P. Smets, P.P. Bonissone, eds.) Morgan & Kaufmann (San Mateo) 61–68.Google Scholar
  3. 3.
    Cano J.E., S. Moral, J.F. Verdegay-López (1992) Propagation of convex sets of probabilities in directed acyclic networks. Proceedings of the IPMU'93 Conference, Mallorca, 289–292.Google Scholar
  4. 4.
    Choquet G. (1953/54) Theorie of capacities. Ann. Inst. Fourier 5, 131–292.Google Scholar
  5. 5.
    Dempster A.P. (1967) Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339.Google Scholar
  6. 6.
    Levi I. (1980) The Enterprise of Knowledge. MIT Press.Google Scholar
  7. 7.
    Levi I. (1985) Imprecision and indeterminacy in probability judgement Philosophy of Science 52, 390–409.Google Scholar
  8. 8.
    Moral S. (1992) Calculating uncertainty intervals from conditional convex sets of probabilities. In: Uncertainty in Artificial Intelligence. Proceedings of the 8th Conference (D. Dubois, M.P. Wellman, B.D'Ambrosio, P. Smets, eds.) Morgan & Kaufmann, San Mateo, 199–206.Google Scholar
  9. 9.
    Moral S., L.M. de Campos (1991) Updating uncertain information. In: Uncertainty in Knowledge Bases (B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh, eds.) Springer Verlag, Lectures Notes in Computer Science N. 521, Berlin, 58–67.Google Scholar
  10. 10.
    Preparata F.P., M.I. Shamos (1985) Computational Geometry. An Introduction. Springer Verlag, New York.Google Scholar
  11. 11.
    Shafer G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton.Google Scholar
  12. 12.
    Snow P. (1991) Improved posterior probability estimates from prior and conditional linear constraint systems. IEEE SMC 21, 464–469.Google Scholar
  13. 13.
    Stirling W., D. Morrel (1991) Convex bayes decision theory. IEEE SMC 21, 163–183.Google Scholar
  14. 14.
    Walley P. (1991) Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Serafín Moral
    • 1
  1. 1.Departamento de Ciencias de la Computación e I.AUniversidad de GranadaGranadaSpain

Personalised recommendations