An imprecision importance measure for uncertainty representations interpreted as lower and upper probabilities, with special emphasis on possibility theory

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

Volumn 226, Issue 6, 2012, Pages 656-665

  Flage, Roger ^a   Aven, Terje ^a   Baraldi, Piero ^b   Zio, Enrico ^b,c  

^a UNIVERSITY OF STAVANGER   (Norway)

^b POLITECNICO DI MILANO   (Italy)

^c ECOLE CENTRALE PARIS   (France)

Author keywords

epistemic uncertainty; importance measure; Imprecision

Indexed keywords

BAYESIAN PERSPECTIVE; COMPONENT LEVELS; EPISTEMIC UNCERTAINTIES; EVIDENCE THEORIES; IMPORTANCE MEASURE; IMPRECISE PROBABILITIES; IMPRECISION; LOWER AND UPPER PROBABILITIES; NUMERICAL EXAMPLE; POSSIBILITY THEORY; PROBABILISTIC REPRESENTATION; PROBABILITY ASSIGNMENT; RELIABILITY PARAMETERS; SUBJECTIVE PROBABILITY; SYSTEM LEVELS; UNCERTAINTY REPRESENTATION;

UNCERTAINTY ANALYSIS;

EID: 84873904142     PISSN: 1748006X     EISSN: 17480078     Source Type: Journal    
DOI: 10.1177/1748006X12467591     Document Type: Conference Paper

References (31)

1. Aven T, Nøkland TE. On the use of uncertainty importance measures in reliability and risk analysis. Rel Engng Sys Saf. 2010 ; 95 (2). 127-133
2. Kaplan S, Garrick BJ. On the quantitative definition of risk. Risk Analysis. 1981 ; 1 (1). 11-27
3. Aven T, Jensen U Stochastic models in reliability. New York: Springer ; 1999 :
4. Rausand M, Høyland A System reliability theory: models, statistical methods, and applications. 2 nd ed.Hoboken, NJ: Wiley-Interscience, 2004. Hoboken, NJ: Wiley-Interscience ; 2004 :
5. Walley P Statistical reasoning with imprecise probabilities. London: Chapman and Hall ; 1991 :
6. Dempster AP. Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat. 1967 ; 38: 325-339
7. Shafer G A mathematical theory of evidence. Princeton University Press ; 1976 :
8. Dubois D, Prade H Possibility theory - an approach to computerized processing of uncertainty. New York: Plenum Press ; 1988 :
9. Zadeh LA. Fuzzy sets. Information and Control. 1965 ; 8: 338-353
10. Berger JO Robustness of Bayesian analyses. Kadane JB, ed. Amsterdam: Elsevier Science ; 1984: 63-144.
11. Ferson S, Kreinovich V, Ginzburg L, et al Constructing probability boxes and Dempster-Shafer structures. Technical Report SAND2002-4015, Sandia National Laboratories, 2003.
12. Weichselberger K. The theory of interval probability as a unifying concept for uncertainty. Int J Approximate Reasoning. 2000 ; 24: 149-170
13. Iman RL. A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Analysis. 1987 ; 7 (1). 21-33
14. Suresh PV, Babar AK, Raj VV. Uncertainty in fault tree analysis: a fuzzy approach. Fuzzy Sets and Systems. 1996 ; 83: 135-141
15. Baraldi P, Zio E. A combined Monte Carlo and possibilistic approach to uncertainty propagation in event tree analysis. Risk Analysis. 2008 ; 28 (5). 1309-1325
16. Liping H, Fuzheng Q. Possibilistic entropy-based measure of importance in fault tree analysis. J Sys Engng Electron. 2009 ; 20 (2). 434-444
17. Dubois D. Possibility theory and statistical reasoning. Compl Stat Data Analysis. 2006 ; 51: 47-69
18. Flage R, Baraldi P, Zio E, et al. On imprecision in relation to uncertainty importance measures. Advances in safety, reliability and risk management. Proceedings of the European Safety and Reliability Conference (ESREL) 2011 ; 2011 Troyes, France ; 18-22 September 2011, pp.2250-2255.
19. Cheok MC, Parry GW, Sherry RR. Use of importance measures in risk-informed regulatory applications. Rel Engng Sys Saf. 1998 ; 60: 213-226
20. Zio E Computational methods for reliability and risk analysis. Hackensack, NJ: World Scientific ; 2009 :
21. Borgonovo E. Measuring uncertainty importance: Investigation and comparison of alternative approaches. Risk Analysis. 2006 ; 26 (5). 1349-1361
22. Apostolakis GE. The concept of probability in safety assessments of technological systems. Science. 1990 ; 250 (4986). 1359-1364
23. Helton JC, Burmaster DE. Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems. Rel Engng Sys Saf. 1996 ; 54: 91-94
24. Dubois D, Prade H. When upper probabilities are possibility measures. Fuzzy Sets and Systems. 1992 ; 49: 65-74
25. Dubois D, Prade H, Sandri S Fuzzy logic: state of the art. Lowen R Roubens M, ed. Dordrecht: Kluwer Academic Publishers ; 1993: 103-112.
26. Baudrit C, Dubois D, Guyonnet D. Joint propagation of probabilistic and possibilistic information in risk assessment. IEEE Trans Fuzzy Systems. 2006 ; 14 (5). 593-608
27. Kalos MH, Whitlock PA Monte Carlo methods. Volume I: basics. Wiley ; 1986 :
28. Pedroni N, Zio E. Empirical comparison of methods for the hierarchical propagation of hybrid uncertainty in risk assessment in presence of dependences. Int J Uncertainty, Fuzziness and Knowledge-Based Systems. 2012 ; 20 (4). 509-557
29. Klir GJ Uncertainty and information: foundations of generalized information theory. Hoboken, NJ: Wiley-Interscience ; 2006 :
30. Klir GJ. Uncertainty and information measures for imprecise probabilities: an overview. Proceedings of the 1st international symposium on imprecise probabilities and their applications (ISIPTA '99) ; 1999 Ghent, Belgium ; 1999. pp. 234-240.
31. Baraldi P, Librizzi M, Zio E, et al. Two techniques of sensitivity and uncertainty analysis of fuzzy expert systems. Expert Systems with Applic. 2009 ; 36 (10). 12461-12471