R. Ahlfeld, B. Belkouchi, and F. Montomoli, SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos, Journal of Computational Physics, vol.320, pp.1-16, 2016.
DOI : 10.1016/j.jcp.2016.05.014

D. A. Alvarez, J. E. Hurtado, and F. Uribe, Estimation of the Lower and Upper Probabilities of Failure Using Random Sets and Subset Simulation, Vulnerability, Uncertainty, and Risk, 2014.
DOI : 10.1061/9780784413609.092

B. M. Ayyub, Elicitation of Expert Opinions for Uncertainty and Risks, 2001.

B. M. Ayyub and G. J. Klir, Uncertainty Modeling and Analysis in Engineering and the Sciences, 2006.
DOI : 10.1201/9781420011456

M. Balesdent, J. Morio, and J. Marzat, Kriging-based adaptive Importance Sampling algorithms for rare event estimation, Structural Safety, vol.44, pp.1-10, 2013.
DOI : 10.1016/j.strusafe.2013.04.001

J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 1985.
DOI : 10.1007/978-1-4757-4286-2

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: a non intrusive approach by regression, Revue europ??enne de m??canique num??rique, vol.15, issue.1-2-3, pp.1-3, 2006.
DOI : 10.3166/remn.15.81-92

G. Blatman and B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.25, issue.2, pp.183-197, 2010.
DOI : 10.1016/j.probengmech.2009.10.003

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, issue.6, pp.2345-2367, 2011.
DOI : 10.1016/j.jcp.2010.12.021

R. H. Byrd, M. E. Hribar, and J. Nocedal, An Interior Point Algorithm for Large-Scale Nonlinear Programming, SIAM Journal on Optimization, vol.9, issue.4, pp.877-900, 1999.
DOI : 10.1137/S1052623497325107
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.7940

P. Chebyshev, Sur les valeurs limites des intégrales, Journal de Mathématiques Pures et Appliquées, Ser, vol.2, pp.19-157, 1874.

S. Chen, K. G. Reyes, M. K. Gupta, M. C. Mcalpine, and W. B. , Optimal Learning in Experimental Design Using the Knowledge Gradient Policy with Application to Characterizing Nanoemulsion Stability, SIAM/ASA Journal on Uncertainty Quantification, vol.3, issue.1, pp.320-345, 2015.
DOI : 10.1137/140971129

E. De-rocquigny, Modelling under risk and uncertainty ? An introduction to statistical, phenomenological and computational methods. Wiley series in probability and statistics, 2012.

A. P. Dempster, Upper and Lower Probabilities Induced by a Multivalued Mapping, The Annals of Mathematical Statistics, vol.38, issue.2, pp.325-339, 1967.
DOI : 10.1214/aoms/1177698950
URL : http://projecteuclid.org/download/pdf_1/euclid.aoms/1177698950

W. Deng, X. Yang, L. Zou, M. Wang, Y. Liu et al., An improved self-adaptive differential evolution algorithm and its application, Chemometrics and Intelligent Laboratory Systems, vol.128, pp.66-76, 2013.
DOI : 10.1016/j.chemolab.2013.07.004

D. Kiureghian, A. , and M. De-stefano, Efficient Algorithm for Second???Order Reliability Analysis, Journal of Engineering Mechanics, vol.117, issue.12, 1990.
DOI : 10.1061/(ASCE)0733-9399(1991)117:12(2904)

D. Kiureghian, A. , and O. Ditlevsen, Aleatory or epistemic? Does it matter? Structural Safety, pp.105-112, 2009.
DOI : 10.1016/j.strusafe.2008.06.020

S. Destercke, D. Dubois, and E. Chojnacki, Unifying practical uncertainty representations. II: Clouds, International Journal of Approximate Reasoning, vol.49, issue.3, pp.664-677, 2008.
DOI : 10.1016/j.ijar.2008.07.004
URL : https://hal.archives-ouvertes.fr/irsn-00311696

S. Dey, T. Mukhopadhyay, H. H. Khodaparast, and S. Adhikari, Fuzzy uncertainty propagation in composites using Gram???Schmidt polynomial chaos expansion, Applied Mathematical Modelling, vol.40, issue.7-8, pp.4412-4428, 2016.
DOI : 10.1016/j.apm.2015.11.038

W. Dong and H. C. Shah, Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, vol.24, issue.1, pp.65-78, 1987.
DOI : 10.1016/0165-0114(87)90114-X

D. Dubois, H. Fargier, and J. Fortin, A generalized vertex method for computing with fuzzy intervals, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), pp.541-546, 2004.
DOI : 10.1109/FUZZY.2004.1375793

D. Dubois and H. Prade, Possibility theory: an approach to computerized processing of uncertainty, 1988.

V. Dubourg, B. Sudret, and J. Bourinet, Reliability-based design optimization using kriging surrogates and subset simulation, Structural and Multidisciplinary Optimization, vol.42, issue.1, pp.673-690, 2011.
DOI : 10.1007/s00158-011-0653-8
URL : https://hal.archives-ouvertes.fr/hal-00587311

V. Dubourg, B. Sudret, and F. Deheeger, Metamodel-based importance sampling for structural reliability analysis, Probabilistic Engineering Mechanics, vol.33, pp.47-57, 2013.
DOI : 10.1016/j.probengmech.2013.02.002
URL : https://hal.archives-ouvertes.fr/hal-00590604

B. Echard, N. Gayton, and M. Lemaire, AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation, Structural Safety, vol.33, issue.2, pp.145-154, 2011.
DOI : 10.1016/j.strusafe.2011.01.002

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, Annals of Statistics, vol.32, pp.407-499, 2004.

M. S. Eldred and L. P. Swiler, Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with application to radiation-hardened electronics part I : algorithms and benchmark results, 2009.

S. Ferson and L. R. Ginzburg, Different methods are needed to propagate ignorance and variability, Reliability Engineering & System Safety, vol.54, issue.2-3, pp.133-144, 1996.
DOI : 10.1016/S0951-8320(96)00071-3

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.1-3, 2004.
DOI : 10.1016/j.ress.2004.03.008

S. Ferson, V. Kreinovich, L. Ginzburg, D. S. Myers, and K. Sentz, Constructing Probability Boxes and Dempster-Shafer Structures, 2003.
DOI : 10.2172/809606

S. Ferson, R. Nelson, J. Hajagos, D. Berleant, J. Zhang et al., Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis, 2004.

A. Forrester, A. Sobester, and A. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

G. Fu, D. Butler, S. Khu, and S. Sun, Imprecise probabilistic evaluation of sewer flooding in urban drainage systems using random set theory, Water Resources Research, vol.106, issue.1-2, p.2534, 2011.
DOI : 10.1029/2009WR008944

W. Gautschi, Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation, 2004.

A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian Data Analysis, 2009.

R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, 2003.
DOI : 10.1007/978-1-4612-3094-6

G. H. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1989.

S. Gunn, Support vector machines for classification and regression, 1998.

J. H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numerische Mathematik, vol.38, issue.1, pp.84-90, 1960.
DOI : 10.1007/BF01386213

Y. He, M. Mirzargar, and R. M. Kirby, Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory, International Journal of Approximate Reasoning, vol.66, pp.1-15, 2015.
DOI : 10.1016/j.ijar.2015.07.002

J. Helton, J. Johnson, and W. Oberkampf, Alternative representations of epistemic uncertainty, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.1-3, 2004.
DOI : 10.1016/j.ress.2004.03.001

J. Helton and W. Oberkampf, Alternative representations of epistemic uncertainty, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.1-3, 2004.
DOI : 10.1016/j.ress.2004.03.001

Z. Hu and X. Du, A Random Field Approach to Reliability Analysis With Random and Interval Variables, ASCE-ASME J. Risk and Uncert. in Engrg. Sys., Part B: Mech. Engrg., vol.1, issue.4, p.41005, 2015.
DOI : 10.1115/1.4030437

A. Kolmogoroff, Confidence Limits for an Unknown Distribution Function, The Annals of Mathematical Statistics, vol.12, issue.4, 1941.
DOI : 10.1214/aoms/1177731684

D. Krige, A statistical approach to some basic mine valuation problems on the Witwatersrand, J. of the Chem., Metal. and Mining Soc. of South Africa, vol.52, issue.6, pp.119-139, 1951.

S. Lee and B. Kwak, Response surface augmented moment method for efficient reliability analysis, Structural Safety, vol.28, issue.3, pp.261-272, 2006.
DOI : 10.1016/j.strusafe.2005.08.003

J. Li and D. Xiu, Computation of failure probability subjected to epistemic uncertainty, 2012.

S. Marelli and B. Sudret, UQLab: A Framework for Uncertainty Quantification in Matlab, Vulnerability, Uncertainty, and Risk, 2014.
DOI : 10.1061/9780784413609.257

S. Marelli, B. Sudret, and E. Zurich, UQLab user manual ? Polynomial chaos expansions, 2015.

G. Matheron, Random Sets and Integral Geometry, 1975.

M. D. Mckay, R. J. Beckman, and W. J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.2, pp.239-245, 1979.

I. Molchanov, The Theory of Random Sets, 2005.

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

R. Moore, Interval analysis, 1966.

M. Moustapha, B. Sudret, J. Bourinet, and B. Guillaume, Quantile-based optimization under uncertainties using adaptive Kriging surrogate models, Structural and Multidisciplinary Optimization, vol.48, issue.10, 2016.
DOI : 10.1007/s00158-016-1504-4
URL : http://arxiv.org/abs/1605.08978

A. Neumaier, Clouds, Fuzzy Sets, and Probability Intervals, Reliable Computing, vol.10, issue.4, pp.249-272, 2004.
DOI : 10.1023/B:REOM.0000032114.08705.cd
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.3756

M. Oberguggenberger and W. Fellin, Reliability bounds through random sets: Non-parametric methods and geotechnical applications, Computers & Structures, vol.86, issue.10, pp.1093-1101, 2008.
DOI : 10.1016/j.compstruc.2007.05.040

H. Rosenbrock, An Automatic Method for Finding the Greatest or Least Value of a Function, The Computer Journal, vol.3, issue.3, pp.175-184, 1960.
DOI : 10.1093/comjnl/3.3.175

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

R. Schöbi and B. Sudret, Imprecise structural reliability analysis using PC-Kriging, Proc. 25th European Safety and Reliability Conference (ESREL2015), 2015.
DOI : 10.1201/b19094-549

R. Schöbi and B. Sudret, Propagation of uncertainties modelled by parametric p-boxes using sparse polynomial chaos expansions, Proc. 12th Int. Conf. on Applications of Stat. and Prob. in Civil Engineering (ICASP12), 2015.

R. Schöbi and B. Sudret, Multi-level meta-modelling in imprecise structural reliability analysis, Proc. 6th Asian-Pacific Symp. Struct. Reliab. (APSSRA'2016), 2016.

R. Schöbi, B. Sudret, and S. Marelli, Rare Event Estimation Using Polynomial-Chaos Kriging, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 2016.
DOI : 10.1061/AJRUA6.0000870

R. Schöbi, B. Sudret, and J. Wiart, POLYNOMIAL-CHAOS-BASED KRIGING, International Journal for Uncertainty Quantification, vol.5, issue.2, pp.171-193, 2015.
DOI : 10.1615/Int.J.UncertaintyQuantification.2015012467

G. Shafer, A mathematical theory of evidence, 1976.

N. Smirnov, On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bulletin de l, 1939.

L. M. Sobol-', On the distribution of points in a cube and the approximate evaluation of integrals, USSR Computational Mathematics and Mathematical Physics, vol.7, issue.4, pp.86-112, 1967.
DOI : 10.1016/0041-5553(67)90144-9

J. Stolfi and L. H. De-figueiredo, An Introduction to Affine Arithmetic, TEMA - Tend??ncias em Matem??tica Aplicada e Computacional, vol.4, issue.3, pp.297-312, 2003.
DOI : 10.5540/tema.2003.04.03.0297
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.3196

R. Storn and K. Price, Differential evolution, a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, vol.11, issue.4, pp.341-359, 1997.
DOI : 10.1023/A:1008202821328

B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models ? Contributions to structural reliability and stochastic spectral methods, 2007.

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

B. Sudret, Polynomials chaos expansions and stochastic finite element methods, 2015.

R. Tibshirani, Regression shrinkage and selection via LASSO, J. Roy. Stat. Soc. B, vol.58, pp.267-288, 1996.
DOI : 10.1111/j.1467-9868.2011.00771.x

F. Tonon, Using random set theory to propagate epistemic uncertainty through a mechanical system, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.1-3, 2004.
DOI : 10.1016/j.ress.2004.03.010

P. Walley, Towards a unified theory of imprecise probability, International Journal of Approximate Reasoning, vol.24, issue.2-3, pp.125-148, 2000.
DOI : 10.1016/S0888-613X(00)00031-1

H. Zhang, H. Dai, M. Beer, and W. Wang, Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method, Mechanical Systems and Signal Processing, vol.37, issue.1-2, pp.137-151, 2013.
DOI : 10.1016/j.ymssp.2012.03.001

H. Zhang, R. L. Mullen, and R. L. Muhanna, Interval Monte Carlo methods for structural reliability, Structural Safety, vol.32, issue.3, pp.183-190, 2010.
DOI : 10.1016/j.strusafe.2010.01.001