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Allocations of Probability

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Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ,volume 219)

Abstract

This paper studies belief functions, set functions which are normalized and monotone of order 8. The concepts of continuity and condensability are defined for belief functions, and it is shown how to extend continuous or condensable belief functions from an algebra of subsets to the corresponding power set. The main tool used in this extension is the theorem that every belief function can be represented by an allocation of probability i.e., by a n-homomorphism into a positive and completely additive probability algebra. This representation can be deduced either from an integral representation due to Choquet or from more elementary work by Revuz and Honeycutt.

Keywords

  • Belief function
  • Allocation of probability
  • Capacity
  • Upper and lower probabilities
  • Condensability
  • Continuity

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References

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Shafer, G. (2008). Allocations of Probability. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-44792-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25381-5

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