Reasoning with imprecise belief structures

International Journal of Approximate Reasoning

Volumn 20, Issue 1, 1999, Pages 79-111

  Denœux, Thierry ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Belief functions; Dempster shafer theory; Evidence theory; Imprecision; Pattern classification; Transferable belief model; Uncertainty modeling

Indexed keywords

EID: 17544395348     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0888-613X(00)88944-6     Document Type: Article

References (42)

1. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics AMS-38 (1967) 325-339.
2. T. Denœux, A k-nearest neighbor classification rule based on Dempster-Shafer theory, IEEE Transactions on Systems, Man and Cybernetics 25 (05) (1995) 804-813.
3. T. Denœux, Analysis of evidence-theoretic decision rules for pattern classification, Pattern Recognition 30 (7) (1997) 1095-1107.
4. T. Denœux, Allowing imprecision in belief representation using fuzzy-valued belief structures, in: Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU'98), Paris, vol. 1, Editions EDK, July 1998, pp. 48-55.
5. T. Denœux, Application du modèle des croyances transférables en reconnaissance de formes, Traitement du Signal 14 (5) (1998) 443-451.
6. T. Denœux, Modeling vague beliefs using fuzzy-valued belief structures, Fuzzy Sets and Systems, in press.
7. D. Dubois, H. Prade, Addition of interactive fuzzy numbers, IEEE Transactions on Automatic Control 26 (4) (1981) 926-936.
8. D. Dubois, H. Prade, The use of fuzzy numbers in decision analysis, in: M.M. Gupta, E. Sanchez (Eds.), Fuzzy Information and Decision Processes, North-Holland, New York, 1982, pp. 309-321.
9. D. Dubois, H. Prade, Properties of measures of information in evidence and possibility theories, Fuzzy Sets and Systems 24 (1987) 161-182.
10. D. Dubois, H. Prade, Possibility Theory: An approach to computerized processing of uncertainty, Plenum Press, New York, 1988.
11. M. Ishizuka, K.S. Fu, Inference procedures under uncertainty for the problem-reduction method, Information Sciences 28 (1982) 179-206.
12. A. Kaufmann, M.M. Gupta, Introduction to fuzzy arithmetic. Theory and applications, International Thomson Computer Press, London, 1991.
13. G.J. Klir, Measures of uncertainty in the Dempster-Shafer theory of evidence, in: R.R. Yager, M. Fedrizzi, J. Kacprzyk (Eds.), Advances in the Dempster-Shafer theory of evidence, Wiley, New York, 1994, pp. 35-49.
14. G.J. Klir, M. Mariano, On the uniqueness of possibilistic measure of uncertainty and information, Fuzzy Sets and Systems 24 (1987) 197-219.
15. G.J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice-Hall, Upper Saddle River, NJ, 1995.
16. M. Lamata, S. Moral, Calculus with linguistic probabilities and beliefs, In: R.R. Yager, M. Fedrizzi, J. Kacprzyk (Eds.), Advances in the Dempster-Shafer theory of evidence, Wiley, New York, 1994, pp. 133-152.
17. E.S. Lee, Q. Zhu, Fuzzy and evidence reasoning, Physica-Verlag, Heidelberg, 1995.
18. H. Ogawa, K.S. Fu, J.T.P. Yao, An inexact inference for damage assessment of existing structures, International Journal of Man-Machine Studies 22 (1985) 295-306.
19. A. Ramer, Uniqueness of information measure in the theory of evidence, Fuzzy Sets and Systems 24 (1987) 183-196.
20. G. Shafer, A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, NJ, 1976.
21. P. Smets, The degree of belief in a fuzzy event, Information Sciences 25 (1981) 1-19.
22. P. Smets, Information content of an evidence, International Journal of Man-Machine Studies 19 (1983) 33-43.
23. P. Smets, The combination of evidence in the Transferable Belief Model, IEEE Transactions on Pattern Analysis and Machine Intelligence 12 (5) (1990) 447-458.
24. P. Smets, Constructing the pignistic probability function in a context of uncertainty, in: M. Henrion, R.D. Schachter, L.N. Kanal, J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence 5, North-Holland, Amsterdam, 1990, pp. 29-40.
25. P. Smets, Resolving misunderstandings about belief functions, International Journal of Approximate Reasoning 6 (1990) 321-344.
26. P. Smets, The transferable belief model and possibility theory, Technical Report TR/IRIDIA/ 90-2, IRIDIA, Bruxelles, 1990.
27. P. Smets, The transferable belief model and random sets, International Journal of Intelligent Systems 7 (1990) 37-46.
28. P. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1-35.
29. P. Smets, Belief induced by the partial knowledge of the probabilities, in: D. Heckerman, D. Poole, R. Lopez de mantaras (Eds.), Uncertainty in AI'94, Morgan Kaufmann, San Mateo, CA, 1994, pp. 523-530.
30. P. Smets, What is Dempster-Shafer's model?, in: R.R. Yager, M. Fedrizzi, J. Kacprzyk (Eds.), Advances in The Dempster-Shafer Theory of Evidence, Wiley, New York, 1994, pp. 5-34.
31. P. Smets, Non-standard probabilistic and non-probabilistic representations of uncertainty, Technical Report TR/IRIDIA/95-2, IRIDIA, Bruxelles, 1995.
32. P. Smets, The normative representation of quantified beliefs by belief functions, Artificial Intelligence 92 (1/2) (1997) 229-242.
33. P. Smets, R. Kennes, The transferable belief model, Artificial Intelligence 66 (1994) 191-243.
34. P. Walley, Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London, 1991.
35. R.R. Yager, Generalized probabilities of fuzzy events from fuzzy belief structures, Information Sciences 28 (1982) 45-62.
36. R.R. Yager, Entropy and specificity in a mathematical theory of evidence, International Journal of general Systems 9 (1983) 249-260.
37. R.R. Yager, Arithmetic and other operations on Dempster-Shafer structures, International Journal of Man-Machine Studies 25 (1986) 357-366.
38. R.R. Yager, On the normalization of fuzzy belief structure, International Journal of Approximate Reasoning 14 (1996) 127-153.
39. R.R. Yager, D.P. Filev, Including probabilistic uncertainty in fuzzy logic controller modeling using Dempster-Shafer theory, IEEE Transactions on Systems, Man and Cybernetics 25 (8) (1995) 1221-1230.
40. J. Yen, Generalizing the Dempster-Shafer theory to fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics 20 (3) (1990) 559-569.
41. L.A. Zadeh, Fuzzy sets and information granularity, in: R.K. Ragade, M.M. Gupta, R.R. Yager (Eds.), Advances in Fuzzy Sets Theory and Applications, North-Holland, Amsterdam, 1979, pp. 3-18.
42. L.M. Zouhal, T. Denœux, An evidence-theoretic k-NN rule with parameter optimization, IEEE Transactions on Systems, Man and Cybernetics - Part C 28 (2) (1998) 263-271.