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Belief functions with nonstandard values

  • Ivan Kramosil
Accepted Papers
  • 109 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1244)

Abstract

The notions of basic probability assignment and belief function, playing the basic role in the Dempster-Shafer model of uncertainty quantification and processing often called Dempster-Shafer theory, are generalized in such a way that their values are not numbers from the unit interval of reals, but rather infinite sequences of real numbers including those greater than one and the negative ones. Within this extended space it is possible to define inverse probability assignments and, consequently, to define the dual operation to the Dempster combination rule, also to assignments ascribing, to the whole space of discourse, the degree of belief “smaller than any positive real number” or “quasi-zero”, in a sense; the corresponding inverse assignments than take “quasi-infinite” values. This approach extends the space of invertible, or non-dogmatic, in the sense introduced by Ph. Smets, basic probability assignments and belief functions, when compared with the other approaches suggested till now.

Keywords

Uncertainty Quantification Belief Function Nonstandard Analysis Extended Space Basic Probability Assignment 
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.

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References

  1. 1.
    P. R. Halmos. Measure Theory. D. Van Nostrand, New York-Toronto-London, 1950.Google Scholar
  2. 2.
    I. Kramosil. Believability and plausibility functions over infinite sets. International Journal of General Systems, 23(2):173–198, 1994.Google Scholar
  3. 3.
    G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey, 1976.Google Scholar
  4. 4.
    P. Smets. The representation of quantified belief by the transferable belief model. Technical Report TR/IRIDIA/94-19.1, Institut de Récherches Interdisciplinaires et de Dévelopments en Intelligence Artificielle, Université Libre de Bruxelles, 1994, 49 pp.Google Scholar
  5. 5.
    P. Smets. The canonical decomposition of a weighted belief. In IJCAI-95 — Proceedings of the 14th International Joint Conference on Artificial Intelligence, Vol. 2, pp. 1896–1901, Montréal, Québec, Canada, August 20–25 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ivan Kramosil
    • 1
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

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