Theory and Decision

, Volume 55, Issue 1, pp 71–83

Objective Belief Functions as Induced Measures

Article

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.

belief function decision under risk induced measure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. Dynkin, E.B. (1965), Markov Processes, Vol. II, Springer.Google Scholar
  3. Epstein, L.G. and Zhang, J. (2001), Subjective probabilities on subjectively unambiguous events, Econometrica 69, 265–306.Google Scholar
  4. Fishburn, P.C. (1982), The Foundations of Expected Utility, D. Reidel, Dordrecht, Holland.Google Scholar
  5. Ghirardato, P. (2001), Coping with ignorance: unforeseen contingencies and non-additive uncertainty. Economic Theory 17, 247–276.Google Scholar
  6. 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
  7. Jaffray, J-Y. (1989), Linear utility theory for belief functions, Operations Research Letters 8, 107–112.Google Scholar
  8. 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.Google Scholar
  9. 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
  10. Mukerji, S. (1997), Understanding the non-additive probability decision models, {tiEconomic Theory} 9, 23–46.Google Scholar
  11. Shafer, G. (1976), A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ. Princeton University Press (1953, 3rd ed.).Google Scholar
  12. Suppes, P. (1966), The probabilistic argument for a non-classical logic of quantum mechanics, Philosophy of Science 33, 14–21.Google Scholar
  13. 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
  14. Zhang, J. (1999), Qualitative probabilities on λ-system, Mathematical Social Sciences 38, 11–20.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.Institute of Policy ana Planning Sciences, University of TsukubaTsukuba, IbarakiJapan

Personalised recommendations