An expectation operator for belief functions in the Dempster–Shafer theoryFootnote^*

* Presented at the 11th Workshop on Uncertainty Processing (WUPES'18), Třeboň, Czech Republic, June 6–9, 2018.

References

• Choquet, G. 1953. “Theory of Capacities.” Annales de l'Institut Fourier 5: 131–295.
   Google Scholar
• Cobb, B. R., and P. P. Shenoy. 2006. “On the Plausibility Transformation Method for Translating Belief Function Models to Probability Models.” International Journal of Approximate Reasoning 41 (3): 314–330.
   Web of Science ®Google Scholar
• Coletti, G., D. Petturiti, and B. Vantaggi. 2019. “Models for Pessimistic Or Optimistic Decisions Under Different Uncertain Scenarios.” International Journal of Approximate Reasoning 105 (2): 305–326.
   Google Scholar
• Dempster, A. P. 1967. “Upper and Lower Probabilities Induced by a Multivalued Mapping.” The Annals of Mathematical Statistics 38 (2): 325–339.
   Google Scholar
• Denoeux, T., and P. P. Shenoy. 2019. “An Interval-Valued Utility Theory for Decision Making with Dempster-Shafer Belief Functions.” Working Paper 336, University of Kansas School of Business, Lawrence, KS.
   Google Scholar
• Ellsberg, D. 1961. “Risk, Ambiguity and the Savage Axioms.” The Quarterly Journal of Economics 75 (2): 643–669.
   Google Scholar
• Fagin, R., and J. Y. Halpern. 1991. “A New Approach to Updating Beliefs.” In Uncertainty in Artificial Intelligence 6, edited by P. Bonissone, M. Henrion, L. Kanal, and J. Lemmer, 347–374. Amsterdam: Elsevier Science.
   Google Scholar
• Gilboa, I., and D. Schmeidler. 1989. “Maxmin Expected Utility with a Non-unique Prior.” Journal of Mathematical Economics 18 (2): 141–153.
   Web of Science ®Google Scholar
• Gilboa, I., and D. Schmeidler. 1994. “Additive Representations of Non-additive Measures and the Choquet Integral.” Annals of Operations Research 52: 43–65.
   Google Scholar
• Halpern, J. Y., and R. Fagin. 1992. “Two Views of Belief: Belief As Generalized Probability and Belief As Evidence.” Artificial Intelligence 54 (3): 275–317.
   Web of Science ®Google Scholar
• Huygens, C. 1657. De ratiociniis in ludo aleæ [English translation, published in 1714].
   Google Scholar
• Jaffray, J.-Y. 1989. “Linear Utility Theory for Belief Functons.” Operations Research Letters 8 (2): 107–112.
   Web of Science ®Google Scholar
• Jiroušek, R., and V. Kratochvíl. 2018. “Comparison of Shenoy's Expectation Operator with Probabilistic Transforms and Perez' Barycenter.” In Proceedings of the 11th Workshop on Uncertainty Processing, edited by V. Kratochvíl and J. Vejnarová, 87–95. Prague.
   Google Scholar
• Jiroušek, R., and P. P. Shenoy. 2018a. “A New Definition of Entropy of Belief Functions in the Dempster-Shafer Theory.” International Journal of Approximate Reasoning 92 (1): 49–65.
   Google Scholar
• Jiroušek, R., and P. P. Shenoy. 2018b. “A Decomposable Entropy of Belief Functions in the Dempster-Shafer Theory.” Working Paper 334, University of Kansas School of Business, Lawrence, KS.
   Google Scholar
• Jiroušek, R., and P. P. Shenoy. 2018c. “A Decomposable Entropy of Belief Functions in the Dempster-Shafer Theory.” In Belief Functions: Theory and Applications, 5th International Conference, BELIEF 2018, vol. 11069 of Lecture Notes in Artificial Intelligence, edited by S. Destercke, T. Denoeux, F. Cuzzolin, and A. Martin, 146–152. Switzerland AG: Springer Nature.
   Google Scholar
• Rockafellar, R. T. 1970. Convex Analysis. Princeton, NJ: Princeton University Press.
   Google Scholar
• Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.
   Google Scholar
• Shafer, G. 1981. “Constructive Probability.” Synthese 48 (1): 1–60.
   Web of Science ®Google Scholar
• Shafer, G. 1982. “Belief Functions and Parametric Models.” Journal of the Royal Statistical Society, Series B 44 (3): 322–352.
   Google Scholar
• Shafer, G. 1990. “Perspectives on the Theory and Practice of Belief Functions.” International Journal of Approximate Reasoning 4 (5–6): 323–362.
   Google Scholar
• Shafer, G. 1992. “Rejoinders to Comments on “Perspectives on the Theory and Practice of Belief Functions”.” International Journal of Approximate Reasoning 6 (3): 445–480.
   Google Scholar
• Shannon, C. E. 1948. “A Mathematical Theory of Communication.” Bell System Technical Journal, 27: 379–423, 623–656.
   Google Scholar
• Shenoy, P. P. 1994. “Conditional Independence in Valuation-based Systems.” International Journal of Approximate Reasoning 10 (3): 203–234.
   Web of Science ®Google Scholar
• Shenoy, P. P. 2018. “An Expectation Operator for Belief Functions in the Dempster-Shafer theory.” In Proceedings of the 11th Workshop on Uncertainty Processing (WUPES'18), Třeboň, Czech Republic, edited by V. Kratochvíl and J. Vejnarová, 165–176. Praha, Czech Republic: MatfyzPress.
   Google Scholar
• Smets, P. 1978. “Un Modele Mathematico-Statistique Simulant Le Processus Du Diagnostic Medical.” PhD thesis, Free University of Brussels.
   Google Scholar
• Smets, P. 2002. “Decision Making in a Context Where Uncertainty is Represented by Belief Functions.” In Belief Functions in Business Decisions, edited by R. P. Srivastava and T. J. Mock, 316–332. Heidelberg: Physica-Verlag.
   Google Scholar
• von Neumann, J., and O. Morgenstern. 1947. Theory of Games and Economic Behavior. 2nd ed. Princeton, NJ: Princeton University Press.
   Google Scholar