Skip to main content
SpringerLink
Log in

Objective Belief Functions as Induced Measures

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

Given a belief function ν on the set of all subsets of prizes, how should ν values be understood as a decision alternative? This paper presents and characterizes an induced-measure interpretation of belief functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chateauneuf, A. and Jaffray, J-Y. (1989), Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Mathematical Social Sciences 17, 263–283.

    Google Scholar 

  • Dynkin, E.B. (1965), Markov Processes, Vol. II, Springer.

  • Epstein, L.G. and Zhang, J. (2001), Subjective probabilities on subjectively unambiguous events, Econometrica 69, 265–306.

    Google Scholar 

  • Fishburn, P.C. (1982), The Foundations of Expected Utility, D. Reidel, Dordrecht, Holland.

    Google Scholar 

  • Ghirardato, P. (2001), Coping with ignorance: unforeseen contingencies and non-additive uncertainty. Economic Theory 17, 247–276.

    Google Scholar 

  • Hendon, E., Jacobsen, H.J., Sloth, B. and Tranaes, T. (1994), Expected utility with lower probabilities, Journal of Risk and Uncertainty 8, 197–216.

    Google Scholar 

  • Jaffray, J-Y. (1989), Linear utility theory for belief functions, Operations Research Letters 8, 107–112.

    Google Scholar 

  • Jaffray, J-Y. (1991), Linear utility theory and belief functions: a discussion, in A. Chikan (ed.), Progress in Decision, Utility and Risk Theory, Kluwer Academic, pp. 221–229.

  • Jaffray, J-Y. and Wakker, P. (1993), Decision making with belief functions: compatibility and incompatibility with the sure-thing principle, Journal of Risk and Uncertainty 7, 255–271.

    Google Scholar 

  • Mukerji, S. (1997), Understanding the non-additive probability decision models, {tiEconomic Theory} 9, 23–46.

  • Shafer, G. (1976), A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ. Princeton University Press (1953, 3rd ed.).

    Google Scholar 

  • Suppes, P. (1966), The probabilistic argument for a non-classical logic of quantum mechanics, Philosophy of Science 33, 14–21.

    Google Scholar 

  • Wakker, P. (2000), Dempster-belief functions are based on the principle of complete ignorance, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 271–284.

    Google Scholar 

  • Zhang, J. (1999), Qualitative probabilities on λ-system, Mathematical Social Sciences 38, 11–20.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Policy ana Planning Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki, 305-8573, Japan

    Yutaka Nakamura

Authors
  1. Yutaka Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yutaka Nakamura.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakamura, Y. Objective Belief Functions as Induced Measures. Theory and Decision 55, 71–83 (2003). https://doi.org/10.1023/B:THEO.0000019053.53742.37

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:THEO.0000019053.53742.37

Search

Navigation