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Linear Utility Theory And Belief Functions: A Discussion

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Progress in Decision, Utility and Risk Theory

Part of the book series: Theory and Decision Library ((TDLB,volume 13))

Abstract

The representation of uncertainty situations - specifically of imprecise risk situations - by belief functions is discussed. It is shown that in such situations decisions themselves are associated with belief functions on the outcome space. The application of von Neumann-Morgenstern linear utility theory to belief functions (which leads to a generalized expected utility criterion) can be justified, owing to a property of the mixture of belief functions.

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References

  1. A. Chateauneuf & J.Y. Jaffray, ‘Some characterizations of lower probabilities and other monotone capacities’, to appear in Mathematical Social Sciences.

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  2. A.P. Dempster, ‘Upper and lower probabilities induced by a multivalued mapping’, Annals of Mathematical Statistics, 38, 325–339 (1967).

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  3. P.C. Fishburn, The foundations of expected utility, D.Reidel Publishing Company, Dordrecht, 1982.

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  4. I.N. Herstein & J. Milnor, ‘An axiomatic approach to measurable utility’, Econometrica, 21, 291–297 (1953).

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  5. J.Y. Jaffray, ‘Application of linear utility thory to belief functions’, in B. Bouchon, L. Saitta & R.R. Yager (Eds), Uncertain and Intelligent Systems, Springer-Verlag, Berlin, 1–8, (1988).

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  6. N.E. Jensen, ‘An introduction to Bernoullian utility theory. I: utility functions’, Swedish Journal of Economics, 69, 163–183 (1967).

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  7. G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton (1976).

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  8. J. von Neumann & O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton (1944).

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© 1991 Springer Science+Business Media Dordrecht

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Jaffray, JY. (1991). Linear Utility Theory And Belief Functions: A Discussion. In: Chikán, A. (eds) Progress in Decision, Utility and Risk Theory. Theory and Decision Library, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3146-9_19

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  • DOI: https://doi.org/10.1007/978-94-011-3146-9_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5387-7

  • Online ISBN: 978-94-011-3146-9

  • eBook Packages: Springer Book Archive

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