Belief functions contextual discounting and canonical decompositions

International Journal of Approximate Reasoning

Volumn 53, Issue 2, 2012, Pages 146-158

  Mercier, David ^a,b   Lefèvre, Éric ^a,b   Delmotte, François ^a,b  

^a UNIV LILLE   (France)

^b UArtois   (France)

Author keywords

Belief functions; Canonical decompositions; Discounting; Reinforcement

Indexed keywords

BELIEF FUNCTION; CANONICAL DECOMPOSITION; CORRECTION MECHANISM; DISCOUNTING; DISJUNCTIVE DECOMPOSITION;

DECOMPOSITION; REINFORCEMENT;

UNCERTAINTY ANALYSIS;

EID: 84855436934     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2011.06.005     Document Type: Conference Paper

References (31)

1. I. Bloch Defining belief functions using mathematical morphology - applications to image fusion under imprecision International Journal of Approximate Reasoning 48 2008 437 465 (Pubitemid 351602154)
2. F. Delmotte, G. Gacquer, Detection of defective sources with belief functions, in: L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay (Eds.), Proceedings of the 12th Information Processing and Management of Uncertainty in Knowledge-Based Systems International Conference (IPMU'08), Torremolinos (Malaga), Spain, June 22-27, 2008, pp. 337-344.
3. A. Dempster Upper and lower probabilities induced by multivalued mapping Annals of Mathematical Statistics AMS-38 1967 325 339
4. T. Denœux Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence Artificial Intelligence 172 2008 234 264 (Pubitemid 350256729)
5. D. Dubois, and H. Prade A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets International Journal of General Systems 12 1986 193 226
6. Z. Elouedi, K. Mellouli, and Ph. Smets Assessing sensor reliability for multisensor data fusion with the transferable belief model IEEE Transactions on Systems, Man and Cybernetics B 34 2004 782 787
7. S. Fabre, A. Appriou, and X. Briottet Presentation and description of two classification methods using data fusion based on sensor management Information Fusion 2 2001 49 71 (Pubitemid 33632550)
8. M. Ha-Duong Hierarchical fusion of expert opinions in the transferable belief model, application to climate sensitivity International Journal of Approximate Reasoning 49 3 2008 555 574
9. A. Kallel, and S. Le Hégarat-Mascle Combination of partially non-distinct beliefs: the cautious adaptive rule International Journal of Approximate Reasoning 50 7 2009 1000 1021
10. J. Klein, C. Lecomte, and P. Mich Hierarchical and conditional combination of belief functions induced by visual tracking International Journal of Approximate Reasoning 51 4 2010 410 428
11. D. Mercier, T. Denœux, M.-H. Masson, A parameterized family of belief functions correction mechanisms, in: L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay (Eds.), Proceedings of the 12th Information Processing and Management of Uncertainty in Knowledge-Based Systems International Conference, IPMU'08, Torremolinos (Malaga), Spain, June 22-27, 2008, pp. 306-313.
12. D. Mercier, B. Quost, and T. Denœux Refined modeling of sensor reliability in the belief function framework using contextual discounting Information Fusion 9 2008 246 258 (Pubitemid 351312921)
13. D. Mercier, G. Cron, T. Denœux, and M.-H. Masson Decision fusion for postal address recognition using belief functions Expert Systems with Applications 36 3, part 1 2009 5643 5653
14. D. Mercier, T. Denœux, M.-H. Masson, Belief function correction mechanisms, in: B. Bouchon-Meunier et al. (Eds.), Studies in Fuzziness and Soft Computing, vol. 249, 2010, pp. 203-222.
15. D. Mercier, Extending the contextual discounting of a belief function thanks to its canonical disjunctive decomposition, in: Proceedings of the 1st Workshop on Belief Functions, paper 61, Brest, France, April 1-2, 2010.
16. N. Milisavljević, I. Bloch, S. van den Broek, and M. Acheroy Improving mine recognition through processing and Dempster-Shafer fusion of ground-penetrating radar data Pattern Recognition 36 2003 1233 1250 (Pubitemid 36178569)
17. R. Muñoz-Salinas, R. Medina-Carnicer, F.J. Madrid-Cuevas, and A. Carmona-Poyato Multi-camera people tracking using evidential filters International Journal of Approximate Reasoning 50 5 2009 732 749
18. F. Périsse, D. Mercier, É. Lefvre, and D. Roger Robust diagnostics of stator insulation based on high frequency resonances measurements IEEE Transactions on Dielectrics and Electrical Insulation 16 5 2009 1496 1502
19. F. Pichon, D. Dubois, T. Denœux, Relevance and truthfulness in information fusion correction and fusion, International Journal of Approximate Reasoning, this issue.
20. M. Rombaut, Decision in multi-obstacle matching process using the theory of belief, in: Proceedings of the 1st International Conference on Advances in Vehicle Control and Safety, AVCS'98, Amiens, France, 1998, pp. 63-68.
21. C. Royere, D. Gruyer, V. Cherfaoui, Data association within belief theory, in: Proceedings of the 3rd International Conference on Information Fusion (FUSION'00), paper TuD29, Paris, France, July 10-13, 2000.
22. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
23. P. Smets Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem International Journal of Approximate Reasoning 9 1993 1 35
24. P. Smets, and R. Kennes The transferable belief model Artificial Intelligence 66 1994 191 243
25. P. Smets What is Dempster-Shafer's model? R.R. Yager, M. Fedrizzi, J. Kacprzyk, Advances in the Dempster-Shafer Theory of Evidence 1994 Wiley New York 5 34
26. P. Smets, The canonical decomposition of a weighted belief, in: Morgan Kaufman (Ed.), Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI'95), San Mateo, California, USA, 1995, pp. 1896-1901.
27. P. Smets The transferable belief model for quantified belief representation D.M. Gabbay, Ph. Smets, Handbook of Defeasible Reasoning and Uncertainty Management Systems vol. 1 1998 Kluwer Academic Publishers Dordrecht, The Netherlands 267 301
28. P. Smets, Data fusion in the transferable belief model, in: Proceedings of the 3rd International Conference on Information Fusion, FUSION'2000, Paris, France, July 10-13, 2000, pp. PS21-PS33.
29. P. Smets The application of the matrix calculus to belief functions International Journal of Approximate Reasoning 31 12 2002 1 30
30. P. Smets Analyzing the combination of conflicting belief functions Information Fusion 8 4 2007 387 412 (Pubitemid 46818141)
31. R.R. Yager Hedging in the combination of evidence Journal of Information and Optimization Science 4 1983 73 81