On the plausibility transformation method for translating belief function models to probability models

International Journal of Approximate Reasoning

Volumn 41, Issue 3, 2006, Pages 314-330

  Cobb, Barry R ^a   Shenoy, Prakash P ^b  

^a VIRGINIA MILITARY INSTITUTE   (United States)

^b UNIVERSITY OF KANSAS   (United States)

Author keywords

Dempster's rule of combination; Dempster Shafer belief functions; Pignistic transformation method; Plausibility transformation

Indexed keywords

FORMAL LOGIC; FUNCTIONS; MATHEMATICAL MODELS; PROBABILITY;

DEMPSTER'S RULE OF COMBINATION; DEMPSTER-SHAFER BELIEF FUNCTIONS; PIGNISTIC TRANSFORMATION METHOD; PLAUSIBILITY TRANSFORMATION;

MATHEMATICAL TRANSFORMATIONS;

EID: 33644864393     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2005.06.008     Document Type: Article

References (31)

1. A. Appriou Probabilités et incertitude en fusion de données multisenseurs Revue Scientifique de la Défense 11 1991 27 40
2. P.L. Bogler Shafer-Dempster reasoning with applications to multisensor target identification systems IEEE Transactions on Systems, Man and Cybernetics 17 6 1987 968 977
3. B.R. Cobb, and P.P. Shenoy A comparison of Bayesian and belief function reasoning Information Systems Frontiers 5 4 2003 345 358
4. B.R. Cobb, P.P. Shenoy, On transforming belief function models to probability models, Working Paper No. 293, School of Business, University of Kansas, Lawrence, KS, 2003. Available from: .
5. B.R. Cobb, and P.P. Shenoy A comparison of methods for transforming belief function models to probability models T.D. Nielsen N.L. Zhang Symbolic and Quantitative Approaches to Reasoning with Uncertainty Lecture Notes in Artificial Intelligence 2711 2003 255 266
6. M. Daniel, Transformations of belief functions to probabilities, in: J. Vejnarová (Ed.), Proceedings of the 6th Workshop on Uncertainty Processing in Expert Systems, 2003, pp. 77-90.
7. A.P. Dempster New methods of reasoning toward posterior distributions based on sample data Annals of Mathematical Statistics 37 1966 355 374
8. A.P. Dempster A generalization of Bayesian inference Journal of the Royal Statistical Society, Series B 30 2 1968 205 247
9. D. Dubois, and H. Prade On several representations of an uncertain body of evidence M.M. Gupta E. Sanchez Fuzzy Information and Decision Processes 1982 North-Holland Amsterdam 167 181
10. D. Ellsberg Risk, ambiguity and the Savage's axioms Quarterly Journal of Economics 75 4 1961 643 669
11. R. Giles Foundations for a possibility theory M.M. Gupta E. Sanchez Fuzzy Information and Decision Processes 1982 North-Holland Amsterdam 83 195
12. J.Y. Halpern, and R. Fagin Two views of belief: belief as generalized probability and belief as evidence Artificial Intelligence 54 1992 275 317
13. J.K. Haspert, Relating Bayesian to Dempster-Shafer analyses, Working Paper, Institute for Defense Analyses, 2001.
14. J.Y. Jaffray Linear utility theory for belief functions Operation Research Letters 8 1989 107 112
15. J. Kohlas, and P.A. Monney A Mathematical Theory of Hints: An Approach to Dempster-Shafer Theory of Evidence Lecture Notes in Mathematical Systems 425 1995 Springer-Verlag Berlin
16. J. Pearl Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference 1988 Morgan Kaufmann San Francisco, CA
17. D. Schmeidler Subjective probability and expected utility without additivity Econometrica 57 1989 571 587
18. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
19. G. Shafer Belief functions and possibility measures J. Bezdek The Analysis of Fuzzy Information 1987 CRC Press Boca Raton, FL 51 84
20. P.P. Shenoy Valuation-based systems: a framework for managing uncertainty in expert systems L.A. Zadeh J. Kacprzyk Fuzzy Logic for the Management of Uncertainty 1992 Wiley New York 83 104
21. P.P. Shenoy, No double counting semantics for conditional independence, in: F.G. Cozman, R. Nan, T. Seidenfeld (Eds.), Proceedings of the Fourth International Symposium on Imprecise Probabilities and their Applications, SIPTA, 2005, pp. 306-314.
22. P.P. Shenoy, G. Shafer, Axioms for probability and belief function propagation, in: R.D. Shachter, T.S. Levitt, J.F. Lemmer, L.F. Kanal (Eds.), Uncertainty in Artificial Intelligence, vol. 4, 1990, pp. 169-198;
23. Reprinted in: J. Pearl, G. Shafer (Eds.), Readings in Uncertain Reasoning, Morgan Kaufmann, San Mateo, CA, pp. 575-610.
24. P. Smets, Constructing the pignistic probability function in a context of uncertainty, in: M. Henrion, R.D. Shachter, L.N. Kanal, J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence, vol. 5, 1990, pp. 29-40.
25. P. Smets Decision making in a context where uncertainty is represented by belief functions R.P. Srivastava T.J. Mock Belief Functions in Business Decisions 2002 Physica-Verlag Heidelberg 316 332
26. P. Smets Decision making in the TBM: the necessity of the pignistic transformation International Journal of Approximate Reasoning 38 2 2005 133 147
27. P. Smets, and R. Kennes The transferable belief model Artificial Intelligence 66 1994 191 234
28. T. Strat Decision analysis using belief functions International Journal of Approximate Reasoning 4 1990 391 417
29. F. Voorbraak A computationally efficient approximation of Dempster-Shafer theory International Journal of Man-Machine Studies 30 1989 525 536
30. P. Walley Belief function representation of statistical evidence The Annals of Statistics 15 4 1987 1439 1465
31. R.R. Yager Decision making under Dempster-Shafer uncertainties International Journal of General Systems 20 1982 233 245