Imprecise reliability by evidential networks

Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability

Volumn 223, Issue 2, 2009, Pages 119-131

  Simon, C ^a   Weber, P ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

Author keywords

Dempster Shafer structure; Evidential networks; Imprecise probabilities; Reliability

Indexed keywords

COMPLEX SYSTEMS; COMPONENT FAILURES; DATA REPRESENTATIONS; DEMPSTER-SHAFER STRUCTURE; DIRECTED ACYCLIC GRAPHS; EVIDENCE THEORIES; EVIDENTIAL NETWORKS; FUZZY FAULT TREE; FUZZY NUMBERS; IMPRECISE KNOWLEDGE; IMPRECISE PROBABILITIES; MONTE CARLO SIMULATION; NUMERICAL STUDIES; RELIABILITY PROBLEMS;

FUZZY RULES; FUZZY SETS; KNOWLEDGE REPRESENTATION; RELIABILITY;

PROBABILITY;

EID: 70349686726     PISSN: 1748006X     EISSN: 17480078     Source Type: Journal    
DOI: 10.1243/1748006XJRR190     Document Type: Article

References (51)

1. L Utkin, F Coolen, G Levitin Ed., New metaheuristics, neural, and fuzzy techniques in reliability. Computational intelligence in reliability engineering (: (Springer) 2007): pp. 261-306
2. K. D Rao, H Kushwaha, A Verma, A Srividya, 'Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies' Reliability Engng System Saf. 92 (7) (2007): 947-956
3. E Zio, N Pedroni, 'Building confidence in the reliability assessment of thermal-hydraulic passive systems' Reliability Engng System Safety 94 (2) (2009): 268-281
4. C Baudrit, D Dubois, 'Practical representations of incomplete probabilistic knowledge' Comp. Statistics Data Analysis 51 (2006): 86-106
5. S Ferson, L Ginzburg, 'Different methods are needed to propagate ignorance and variability' Reliability Engng System Saf. 54 (1996): 133-144
6. J. C Helton, W. L Oberkampf, 'Alternative representations of epistemic uncertainty' Reliability Engng System Saf. 85 (2004): 1-10
7. D Dubois, H Prade, Possibility theory. An approach to computerized processing of uncertainty (New York: Plenum Press 1988)
8. S Ferson, V Kreinovich, L Ginzburg, D Myers, K Sentz, Constructing probability boxes and Dempster-Shafer structures. Sandia National Laboratory Technical Report, 2002
9. G Shafer, A mathematical theory of evidence (New York: Princeton University Press 1976)
10. P Walley, Statistical reasoning with imprecise probabilities (London: Chapman & Hall 1991)
11. M Sallak, C Simon, J.-F Aubry, 'A fuzzy probabilistic approach for determining safety integrity level' IEEE Trans. Fuzzy Systems 16 (1) (2008): 239-248
12. A Neumaier, 'Clouds, fuzzy sets and probability intervals' Reliability Computing 10 (2004): 249-272
13. P Limbourg, D Germann, 'Reliability assessment and optimization under uncertainty in the Dempster-Shafer framework' (2004)
14. P Smets, F Kornreich, P Block, H Bernard, R Vainsel, J. H Van Bemel Ed., J. L Willems Ed., 'Fuzzy diagnostic, degrees of belief and utility' Trends in computer processed ECG (: 1977): pp. 257-259
15. P Smets, J Anderson Ed., 'Theory of evidence and medical diagnostic' Medical informatics Europe 78 (Berlin: Springer Verlag 1978): pp. 285-291
16. M.-H Masson, T Denoeux, 'Clustering interval-valued proximity data using belief functions' Pattern Recognition Lett. 25 (2) (2004): 163-171
17. F Tonon, 'Using random set theory to propagate epistemic uncertainty through a mechanical system' Reliability Engng System Saf. 85 (2004): 169-181
18. C Simon, P Weber, A Evsukoff, 'Bayesian networks inference algorithm to implement Dempster-Shafer theory in reliability analysis' Reliability Engng System Saf. 93 (7) (2008): 950-963
19. U Rakowsky, U Gocht, 'Reasoning in reliability centred maintenance based on a Dempster-Shafer approach' J. Risk and Reliability 222 (O4) (2008): 605-612
20. J. Y Halpern, R Fagin, 'Two views of belief: belief as generalized probability and belief as evidence' Artif. Intell. 54 (3) (1992): 275-317
21. L. V Utkin, 'Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model' Fuzzy Sets and Systems 154 (3) (2005): 413-431
22. A. P Dempster, 'Upper and lower probabilities induced by a multivalued mapping' Ann. Mathl Statists 38 (1967): 325-339
23. K Cai, C Wen, M Zhang, 'Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context' Fuzzy Sets and Systems 42 (1991): 145-172
24. K.-Y Cai, C.-Y Wen, M.-L Zhang, 'Fuzzy states as a basis for a theory of fuzzy reliability' Microelectronics and Reliability 33 (15) (1993): 2253-2263
25. K.-Y Cai, 'System failure engineering and fuzzy methodology: An introductory overview' Fuzzy Sets and Systems 83 (2) (1996): 113-133
26. J Buckley, Fuzzy probabilities (New York: Springer Verlag 2005)
27. L. A Zadeh, 'Fuzzy sets' Inf. Control (: 1965): 338-353
28. J Kholas, P Monney, A mathematical theory of hints: an approach to Dempster-Shafer theory of evidence (New York: Springer Verlag 1995)
29. P Smets, R Kennes, 'The transferable belief model' Artificial Intelligence 66 (1994): 191-243
30. K Sentz, S Ferson, Combination of evidence in Dempster-Shafer theory. Sandia National Laboratory Technical Report, 2002
31. E Ouzounova, Incertitude et mesure de performance: Une nouvelle approche à travers la théorie mathématique des indications. PhD dissertation, Faculté des Sciences Economiques et Sociales, Université de Freiburg, Switzerland 2005
32. M. H Duong, Modéle de précaution en économie: introduction aux probabilities imprecises. PhD Dissertation, Université de Paris I- Panthon Sorbonne 2005
33. G. J Klir, T. A Folger, Fuzzy sets, uncertainty, and information (Upper Saddle River, NJ: Prentice-Hall 1987)
34. B. A Chokr, V. Y Kreinovich, 'How far are we from the complete knowledge? Complexity of knowledge acquisition in the Dempster-Shafer approach' Advances in the Dempster-Shafer theory of evidence (New York: John Wiley 1994): pp. 555-576
35. A.-O Boudraa, A Bentabet, F Salzenstei, L Guillon, 'Dempster-Shafer's basic probability assignment based on fuzzy membership functions' Electronic Lett. Computer Vision and Image Analysis 4 (1) (2004): 1-9
36. I Gilboa, D Schmeidler, 'Maximin expected utility with non-unique prior' J. Mathl Econ. 18 (1989): 141-153
37. G. J Klir, M Wierman, 'Uncertainty-based information; elements of generalized information theory' Studies in fuzziness and soft-computing (Heidelberg: Physica-Verlag 1998): p. 168-
38. P Smets, D Heckerman Ed., D Poole Ed., R. L de Mantaras Ed., 'Belief induced by the knowledge of some probabilities' Uncertainty in AI'94 (San Mateo, California: Morgan Kaufmann 1994): pp. 523-530
39. G Klir, B Yuan, Fuzzy sets and fuzzy logic. Theory and applications (Upper Saddle River, NJ: Prentice Hall 1995)
40. M Guth, 'A probability foundation for vagueness and imprecision in fault tree analysis' IEEE Trans Reliability 40 (5) (1991): 563-570
41. Y Cheng, 'Uncertainty in fault tree analysis' Tamkang J. Sci. Engng 3 (1) (2000): 23-29
42. J Hall, J Lawry, 'Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis' ()
43. U. K Rakowsky, 'Fundamentals of the Dempster-Shafer theory and its applications to system safety and reliability modelling' ()
44. P Smets, 'The application of the matrix calculus to belief functions' Int. J. Approximate Reasoning 31 (2002): 1-30
45. P Smets, 'Probability of provability and belief functions' Logique et Analyse 133 (1991): 177-195
46. C Simon, M Sallak, J.-F Aubry, 'SIL allocation of SIS by aggregation of experts' opinions' (2007)
47. F Jensen, An introduction to Bayesian networks (London: University Press 1996)
48. A Bobbio, L Portinale, M Minichino, E Ciancamerla, 'Improving the analysis of dependable systems by mapping fault trees into Bayesian networks' Reliability Engng System Saf. 71 (3) (2001): 249-260
49. H Boudali, J Dugan, 'A discrete-time Bayesian network reliability modeling and analysis framework' Reliability Engng System Saf. 87 (2005): 337-349
50. A Villemeur, Reliability, availability, maintainability safety assessment: methods and techniques (New York: John Wiley 1992)
51. Translated from French edition by A. Cartier and Lartisien M.C. J Torres-Toledano, L Sucar, H Coelho Ed., 'Bayesian networks for reliability of complex systems' Progress in artificial intelligence, IBERAMIA'98 (New York: Springer-Verlag 1998): pp. 195-206