M. Anoop, B. Rao, K. Gopalakrishnan, and S. , Conversion of probabilistic information into fuzzy sets for engineering decision analysis, Computers & Structures, vol.84, issue.3-4, pp.141-155, 2006.
DOI : 10.1016/j.compstruc.2005.09.017

G. E. Apostolakis, The concept of probability in safety assessments of technological systems, Science, vol.250, issue.4986, p.813, 1990.
DOI : 10.1126/science.2255906

G. E. Apostolakis and S. Kaplan, Pitfalls in risk calculations, Reliability Engineering, vol.2, issue.2, p.815, 1981.
DOI : 10.1016/0143-8174(81)90019-6

. Wheeler, Handbook of Parameter Estimation for Probabilistic Risk Assessment. 818 NUREG/CR-6823, SAND2003- 819 3348P, Sandia National Laboratories, p.820, 2003.

T. Aven, On the Need for Restricting the Probabilistic Analysis in Risk Assessments to 821, 2010.

T. Aven, Interpretations of alternative uncertainty representations in a reliability and risk 823 analysis context. Reliability Engineering & System Safety, pp.353-360, 2011.

E. Aven and . Zio, Some considerations on the treatment of uncertainties in risk assessment for 825 practical decision making, Reliability Engineering and System Safety, vol.96, issue.1, pp.826-64, 2011.

I. Baudrit, D. Couso, and . Dubois, Joint propagation of probability and possibility in risk analysis: Towards a formal framework, International Journal of Approximate Reasoning, vol.45, issue.1, pp.82-105, 2007.
DOI : 10.1016/j.ijar.2006.07.001

D. Baudrit, D. Dubois, and . Guyonnet, Joint Propagation and Exploitation of Probabilistic and 835, 2006.

D. Baudrit, N. Dubois, and . Perrot, Representing parametric probabilistic models tainted with 838 imprecision, Fuzzy Sets and System, pp.1913-1928, 2008.

M. Bayarri and J. Berger, Quantifying surprise in the data and model verification, p.840, 1999.

M. Bayarri and J. Berger, P Values for Composite Null Models, Journal of the American Statistical Association, vol.95, issue.452, pp.1127-1169, 2000.
DOI : 10.2307/2669749

T. Bedford and R. Cooke, Probabilistic Risk Analysis. Foundations and Methods, p.843, 2001.

M. Beer, Engineering quantification of inconsistent information, International Journal of Reliability and Safety, vol.3, issue.1/2/3, p.845, 2009.
DOI : 10.1504/IJRS.2009.026840

M. Beer, Fuzzy probability theory, in: Encyclopedia of, Complexity and Systems Science, vol.8476, pp.4047-4059, 2009.

M. Beer and S. Ferson, Special issue of Mechanical Systems and Signal Processing 849 "Imprecise probabilities -What can they add to engineering analyses, Mechanical Systems 850 and Signal Processing, pp.1-3, 2013.

M. Beer, S. Ferson, and V. Kreinovich, Imprecise probabilities in engineering analyses, Mechanical Systems and Signal Processing, vol.37, issue.1-2, p.852, 2013.
DOI : 10.1016/j.ymssp.2013.01.024

M. Beer, Y. Zhang, S. T. Quek, and K. K. Phoon, Reliability analysis with scarce information, p.854, 2013.

M. Beer, F. A. Diazdelao, E. Patelli, and S. K. Au, Conceptual comparison of Bayesian 857 approaches and imprecise probabilities, Computational 858, 2014.

M. Beer, I. A. Kougioumtzoglou, and E. Patelli, Emerging Concepts and Approaches for 860, 2014.

H. Atamturktur and B. Moaveni, Updating for Probabilistic Damage Identification, p.866

C. Papadimitriou and T. Schoenherr, Model validation and uncertainty quantification, p.867
URL : https://hal.archives-ouvertes.fr/hal-01022305

J. M. Bernard, An introduction to the imprecise Dirichlet model for multinomial data, International Journal of Approximate Reasoning, vol.39, issue.2-3, p.869, 2005.
DOI : 10.1016/j.ijar.2004.10.002

D. Blockley, Analysing uncertainties: Towards comparing Bayesian and interval probabilities', Mechanical Systems and Signal Processing, vol.37, issue.1-2, pp.30-42, 2013.
DOI : 10.1016/j.ymssp.2012.05.007

J. J. Buckley, Fuzzy probabilities ? new approach and applications, Studies in Fuzziness, 2005.

P. D. Congdon, Applied Bayesian Hierarchical Methods, 2010.
DOI : 10.1201/9781584887218

F. P. Coolen and L. V. Utkin, Imprecise Probability, pp.881-1959, 2007.
DOI : 10.1007/978-3-642-04898-2_296

I. Couso and D. Dubois, On the Variability of the Concept of Variance for Fuzzy Random 883, 2009.

I. Couso, E. Miranda, and G. De-cooman, A Possibilistic Interpretation of the Expectation of a 885, 2004.

R. Fuzzy and . Variable, In: Soft Methodology and Random Information Systems, p.886

I. Couso, S. Montes, and P. Gil, The necessity of the strong alpha-cuts of a fuzzy set, p.888, 2001.

I. Couso and L. Sánchez, Higher order models for fuzzy random variables, Fuzzy Sets and 890, Systems, vol.159, pp.237-258, 2008.

I. Couso and L. Sánchez, Upper and lower probabilities induced by a fuzzy random variable, Fuzzy Sets and Systems, vol.165, issue.1, p.892, 2011.
DOI : 10.1016/j.fss.2010.10.005

L. G. Crespo, S. P. Kenny, and D. P. Giesy, Reliability analysis of polynomial systems subject to p-box uncertainties, Mechanical Systems and Signal Processing, vol.37, issue.1-2, pp.121-136, 2013.
DOI : 10.1016/j.ymssp.2012.08.012

T. Denoeux, Likelihood-based belief function: Justification and some extensions to low 896, 2014.

D. Dubois, Possibility theory and statistical reasoning, Computational Statistics & Data Analysis, vol.51, issue.1, 2006.
DOI : 10.1016/j.csda.2006.04.015

D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, p.904, 1980.

D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of 906, 1988.

D. Dubois and H. Prade, Bayesian conditioning in possibility theory. Fuzzy Sets and Systems, pp.92-223, 1997.

D. Dubois, . Prade, and S. Sandri, On Possibility/Probability Transformations, 1993.
DOI : 10.1007/978-94-011-2014-2_10

D. Dubois, H. Prade, and P. Smets, A definition of subjective possibility, International Journal of Approximate Reasoning, vol.48, issue.2, p.913, 2008.
DOI : 10.1016/j.ijar.2007.01.005

D. Dubois, S. Moral, and H. Prade, A semantics for possibility theory based on likelihoods, Proceedings of 1995 IEEE International Conference on Fuzzy Systems. The International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium, p.915, 1997.
DOI : 10.1109/FUZZY.1995.409891

A. W. Edwards, Likelihood, Expanded Edition., Biometrics, vol.49, issue.4, p.917, 1992.
DOI : 10.2307/2532282

R. Féron, Ensembles aléatoires flous, CR. Acad. Sc. paris -Série A, vol.282, pp.903-906, 1976.

S. Ferson, Bayesian methods in risk assessment, 2005.

S. Ferson and J. G. Hajagos, Arithmetic with uncertain numbers: rigorous and (often) best possible answers, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.135-152, 2004.
DOI : 10.1016/j.ress.2004.03.008

. Oberkampf, Dependence in probabilistic modeling, Dempster-Shafer theory, and 931 probability bounds analysis, p.932, 2004.

W. T. Ferson and . Tucker, Sensitivity in risk analyses with uncertain numbers, 2006.

P. Ferson, T. L. Van-den-brink, K. Estes, R. Gallagher, F. O-'connor et al., Bounding 935 uncertainty analyses In: Application of uncertainty analysis to ecological risks of pesticides, p.936, 2010.

R. Flage, T. Aven, and E. Zio, Alternative representations of uncertainty in reliability and risk 939 analysis ? review and discussion, p.940, 2009.

S. Valencia, Safety, reliability and risk analysis. Theory, methods 941 and applications, Proceedings of the European safety and reliability conference 2009, pp.22-25, 2008.

P. Flage, E. Baraldi, T. Zio, and . Aven, Possibility-probability transformation in comparing 944 different approaches to the treatment of epistemic uncertainties in a fault tree analysis, p.945, 2010.

P. Flage, E. Baraldi, T. Zio, and . Aven, Probability and Possibility-Based Representations of Uncertainty in Fault Tree Analysis, Risk Analysis, vol.2, issue.1, pp.121-154, 2013.
DOI : 10.1111/j.1539-6924.2012.01873.x

URL : https://hal.archives-ouvertes.fr/hal-00926381

A. Gelman, Bayesian data analysis, p.952, 2004.

A. Gelman, Prior distributions for variance parameters in hierarchical models, p.953, 2006.

A. Gelman, . Meng, . Xl, and H. Stern, Posterior predictive assessment of model fitness via 955 realized discrepancies, pp.733-806, 1996.

A. Gelman, D. Van-dyk, Z. Huang, and W. J. Boscardin, Using Redundant Parameterizations to 957, 2008.

J. Gill, Bayesian methods: a social and behavioral sciences approach, p.960, 2002.

D. Guyonnet, B. Bourgine, D. Dubois, H. Fargier, B. Côme et al., Hybrid approach 962 for addressing uncertainty in risk assessments, Journal of the Environmental Engineering, vol.963, 2003.

J. D. Helton, W. L. Johnson, C. B. Oberkampf, and . Storlie, A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3980-98, 2007.
DOI : 10.1016/j.cma.2006.10.049

Y. Hou and B. Yang, Probability-possibility transformation for small sample size data, 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, p.971, 2010.
DOI : 10.1109/FSKD.2010.5569396

A. Jalal-kamali and V. Kreinovich, Estimating correlation under interval uncertainty, Mechanical Systems and Signal Processing, vol.37, issue.1-2, p.974, 2013.
DOI : 10.1016/j.ymssp.2012.12.003

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.3581

J. S. Jaworska and T. Aldenberg, Estimation of HC5 taking into account uncertainties of 976 individual dose response curves and species sensitivity distribution, Presentation at the 2000 977 Society for Risk Analysis annual meeting, 2000.

J. Valen and E. , A Bayesian ? 2 test for goodness-of-fit, Ann Stat, vol.32, pp.2361-84, 2004.

M. H. Kalos and P. A. Whitlock, Monte Carlo methods. Volume I: Basics, p.981, 1986.

D. L. Kelly and C. L. Smith, Bayesian inference in probabilistic risk assessment???The current state of the art, Reliability Engineering & System Safety, vol.94, issue.2, pp.628-643, 2009.
DOI : 10.1016/j.ress.2008.07.002

E. Kentel and M. M. , Probabilistic-fuzzy health risk modeling, Stochastic Environmental Research and Risk Assessment, vol.18, issue.5, p.987, 2004.
DOI : 10.1007/s00477-004-0187-3

E. Kentel and M. M. , Risk tolerance measure for decision-making in fuzzy analysis: a health risk assessment perspective, Stochastic Environmental Research and Risk Assessment, vol.1, issue.4, pp.405-417, 2007.
DOI : 10.1007/s00477-006-0073-2

B. Klir and . Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, 1995.

I. O. Kozine and L. V. Utkin, Processing unreliable judgements with an imprecise hierarchical model, Risk Decision and Policy, vol.7, issue.3, pp.325-339, 2002.
DOI : 10.1017/S1357530902000716

H. Kwakernaak, Fuzzy Random Variables-I. Definitions and Theorems, Information 1000, Sciences, vol.15, pp.1-29, 1978.
DOI : 10.1016/0020-0255(78)90019-1

URL : http://purl.utwente.nl/publications/68407

S. Lapointe and B. Bobeè, Revision of possibility distributions: A Bayesian inference pattern, Fuzzy Sets and Systems, vol.116, issue.2, p.1002, 2000.
DOI : 10.1016/S0165-0114(98)00367-4

L. Duy, T. D. Vasseur, D. Couplet, M. Dieulle, L. Bérenguer et al., A study on updating 1004 belief functions for pa-rameter uncertainty representation in Nuclear Probabilistic Risk, 1005.

P. Limbourg and E. De-rocquigny, Uncertainty analysis using evidence theory ? confronting 1009, 2010.

D. V. Lindley, The philosophy of statistics. The Statistician, pp.293-337, 2000.

D. V. Lindley, Understanding uncertainty, p.1013, 2006.
DOI : 10.1002/0470055480

URL : http://dx.doi.org/10.1016/s1369-7021(02)05122-2

A. Masegosa, Imprecise probability models for learning multinomial distributions 1014 from data. Applications to learning credal networks, International Journal of Approximate, 1015.

M. H. Masson and T. Denoeux, Inferring a possibility distribution from empirical data, Fuzzy Sets and Systems, vol.157, issue.3, p.1017, 2006.
DOI : 10.1016/j.fss.2005.07.007

G. Mauris, Inferring a Possibility Distribution from Very Few Measurements, 1019.
DOI : 10.1007/978-3-540-85027-4_12

C. H. Mehl, P-boxes for cost uncertainty analysis. Mechanical Systems and Signal 1022, 2013.

I. Molchanov, Theory of Random Sets, 1024.

B. Möller and M. Beer, Fuzzy Randomness: Uncertainty in Civil Engineering and 1025, 2004.
DOI : 10.1007/978-3-662-07358-2

B. Möller and M. Beer, Engineering computation under uncertainty ??? Capabilities of non-traditional models, Computers & Structures, vol.86, issue.10, pp.1024-1041, 2008.
DOI : 10.1016/j.compstruc.2007.05.041

B. Moller, W. Graf, and M. Beer, Safety assessment of structures in view of fuzzy randomness, Computers & Structures, vol.81, issue.15, pp.1567-1582, 1029.
DOI : 10.1016/S0045-7949(03)00147-0

B. Moller, M. Beer, W. Graf, and J. U. Sickert, Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness, Computers & Structures, vol.84, issue.8-9, pp.585-603, 1032.
DOI : 10.1016/j.compstruc.2005.10.006

S. Moral, Comments on " Likelihood-based belief function: Justification and some extensions 1034 to low-quality data " by Thierry Denoeux, International Journal of Approximate Reasoning, p.1035, 2014.

G. Muscolino and A. Sofi, Bounds for the stationary stochastic response of truss structures 1037 with uncertain-but-bounded parameters, 1038 163-181. 1039 NUREG-CR-6850, 2005. EPRI/NRC-RES Fire PRA methodology for nuclear power facilities, p.1040, 2013.

S. Pannier, M. Waurick, W. Graf, and M. Kaliske, Solutions to problems with imprecise 1044 data " -An engineering perspective to generalized uncertainty models, Mechanical Systems 1045 and Signal Processing, pp.105-120, 2013.

A. Pasanisi, E. De-rocquigny, N. Bousquet, and E. Parent, Some useful features of the Bayesian 1047 setting while dealing with uncertainties in industrial practice, Proceedings of the ESREL, 2009.

A. Pasanisi, M. Keller, and M. Parent, Estimation of a quantity of interest inuncertainty 1050 analysis: Some help from Bayesian decision theory, Reliability Engineering and System, 1051.

N. Pedroni and E. Zio, Empirical comparison of methods for the hierarchical propagation of 1053 hybrid uncertainty in risk assessment, in presence of dependences, International Journal, 1054.

. Uncertainty, Fuzziness and Knowledge-Based Systems, pp.509-557, 2012.

N. Pedroni, E. Zio, A. Pasanisi, and M. Couplet, Bayesian update of the parameters of probability 1059 distributions for risk assessment in a two-level hybrid probabilistic-possibilistic uncertainty 1060 framework, p.1061, 2014.

M. L. Puri and D. A. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis, 1066.

D. Quaeghebeur and . Cooman, Imprecise probability models for inference in exponential 1068 families, Electronic Proceedings of the 4th International Symposium on Imprecise 1069 Probabilities and Their Applications, p.1070, 2005.

D. Ralescu, Average level of a fuzzy set, pp.119-1072, 2002.
DOI : 10.1007/978-3-7908-1800-0_8

S. G. Reid, Probabilistic confidence for decisions based on uncertain reliability estimates, Mechanical Systems and Signal Processing, vol.37, issue.1-2, 1074.
DOI : 10.1016/j.ymssp.2012.07.016

S. Sankararaman and S. Mahadevan, Distribution type uncertainty due to sparse and imprecise data, Mechanical Systems and Signal Processing, vol.37, issue.1-2, pp.182-198, 2013.
DOI : 10.1016/j.ymssp.2012.07.008

S. Sentz and . Ferson, Combination of Evidence in Dempster-Shafer Theory, 1078.
DOI : 10.2172/800792

M. Serrurier and H. Prade, Maximum-Likelihood Principle For Possibility Distributions, 1080.

K. E. Shirley and A. Gelman, Hierarchical models for estimating state and demographic trends in US death penalty public opinion, Journal of the Royal Statistical Society: Series A (Statistics in Society), vol.26, issue.1, pp.1-28, 2015.
DOI : 10.1111/rssa.12052

N. Siu and D. Kelly, Bayesian parameter estimation in probabilistic risk assessment, Reliability 1085 Engineering and System Safety, pp.89-116, 1998.
DOI : 10.1016/S0951-8320(97)00159-2

P. Smets, Belief Functions: The Disjunctive Rule of Combination and the Generalized 1087, 1993.

M. &. Stein and . Beer, Bayesian quantification of inconsistent information, 1089.

M. Stein, M. Beer, and V. Kreinovich, Bayesian approach for inconsistent information, Information Sciences, vol.245, p.1092, 2013.
DOI : 10.1016/j.ins.2013.02.024

R. Viertl, Statistical Methods for Non-Precise Data, Boca Raton, p.1100, 1996.
DOI : 10.1007/978-3-642-04898-2_546

R. Viertl, On Statistical Inference for Non-Precise Data, Environmetrics, vol.1, issue.5, pp.541-568, 1997.
DOI : 10.1002/(SICI)1099-095X(199709/10)8:5<541::AID-ENV269>3.0.CO;2-U

R. Viertl, Statistics and integration of fuzzy functions, Environmetrics, vol.8, issue.4, pp.487-491, 1999.
DOI : 10.1002/(SICI)1099-095X(199907/08)10:4<487::AID-ENV369>3.0.CO;2-#

R. Viertl, Foundations of Fuzzy Bayesian Inference, Journal of Uncertain Systems, vol.2, issue.3, pp.1104-187, 2008.

R. Viertl, Fuzzy Bayesian Inference, Soft Methods for Handling 1106 Variability and Imprecision, ASC 48, pp.10-15, 2008.

R. Viertl, Statistical Methods for Fuzzy Data, p.1108, 2011.
DOI : 10.1002/9780470974414

R. Viertl and D. Hareter, Fuzzy information and imprecise probability, ZAMM, vol.32, issue.10-11, p.1109, 2004.
DOI : 10.1002/zamm.200410152

R. Viertl and D. Hareter, Generalized Bayes? theorem for non-precise a-priori distribution, Metrika, vol.59, issue.3, p.1111, 2004.
DOI : 10.1007/s001840300283

R. Viertl and H. Hule, On Bayes' theorem for fuzzy data, Statistical Papers, vol.32, issue.1, p.1113, 1991.
DOI : 10.1007/BF02925485

P. Walley, Statistical reasoning with imprecise probabilities, p.1114, 1991.
DOI : 10.1007/978-1-4899-3472-7

P. Walley, Inferences from multinomial data: learning about a bag of marbles (with 1115 discussion, J. R. Stat. Soc. B, vol.58, pp.3-57, 1996.

G. Walter, A. , and T. , Imprecision and Prior-Data Conflict in Generalized Bayesian Inference, Journal of Statistical Theory and Practice, vol.58, issue.1, 1117.
DOI : 10.1080/15598608.2009.10411924

K. Weichselberger, The theory of interval-probability as a unifying concept for uncertainty, International Journal of Approximate Reasoning, vol.24, issue.2-3, p.1119, 2000.
DOI : 10.1016/S0888-613X(00)00032-3

H. Zhang, H. Dai, M. Beer, W. , and W. , Structural reliability analysis on the basis of 1121 small samples: An interval quasi-Monte Carlo method, p.1122, 2013.