T. and ?. {0, m} such that x, y ? B i by the definitions of the relation ?, ? ? and the sets B 0

?. If-a-ij-?-b-s and . {1, m} then we have [a ij ] P ? [a i ] or [a ij ] = [a i ] because (P ? I ? M ) contains no strict cycle and by the definitions of P ? and ?. Hence, a i ? B r , r ? s. The same argument is

?. If-l and . {j, k} then [i ? j = i if l = j] or [i ? k = i if l = k]. So we have a il ? a i . Hence not, because {P, I} satisfies 2-MOPI

C. A. References, F. Bana-e-costa, . Nunes, J. Silva, and . Vansnick, Conflict dissolution in the public sector: A case-study, European Journal of Operational Research, vol.130, pp.388-401, 2001.

C. A. Bana-e-costa, E. C. Correa, J. Corte, and J. Vansnick, Facilitating bid evaluation in public call for tenders: a socio-technical approach, Omega, vol.30, issue.3, pp.227-242, 2002.
DOI : 10.1016/S0305-0483(02)00029-4

C. A. Bana-e-costa, J. Corte, and J. Vansnick, On the mathematical foundations of MACBETH. Multiple Criteria Decision Analysis: State of the Art Surveys, pp.409-437, 2005.

L. Berrah and V. Clivillé, Towards an aggregation performance measurement system model in a supply chain context, Computers in Industry, vol.58, issue.7, pp.709-719, 2007.
DOI : 10.1016/j.compind.2007.05.012
URL : https://hal.archives-ouvertes.fr/hal-00637615

A. Chateauneuf, Modeling attitudes towards uncertainty and risk through the use of choquet integral, Annals of Operations Research, vol.1, issue.1, pp.3-20, 1994.
DOI : 10.1007/BF02032158

A. Chateauneuf, Ellsberg Paradox Intuition and Choquet Expected Utility, Mathematical models for handling partial knowledge in artificial intelligence, pp.1-20, 1995.
DOI : 10.1007/978-1-4899-1424-8_1

A. Chateauneuf and J. Y. Jaffray, Some characterizations of lower probabilities and other monotone capacities through the use of M??bius inversion, Mathematical Social Sciences, vol.17, issue.3, pp.263-283, 1989.
DOI : 10.1016/0165-4896(89)90056-5

A. Chateauneuf, R. Kast, and A. Lapied, Conditioning capacities and choquet integrals: The role of comonotony, Theory and Decision, vol.51, issue.2/4, pp.367-386, 2004.
DOI : 10.1023/A:1015567329595

A. Chateauneuf, M. Grabisch, and A. Rico, Modeling attitudes toward uncertainty through the use of the Sugeno integral, Journal of Mathematical Economics, vol.44, issue.11, pp.1084-1099, 2008.
DOI : 10.1016/j.jmateco.2007.09.003
URL : https://hal.archives-ouvertes.fr/halshs-00327700

. Choquet, Theory of capacities Annales de l'Institut Fourier, pp.131-295, 1953.

V. Clivillé, L. Berrah, and G. Mauris, Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method, International Journal of Production Economics, vol.105, issue.1, pp.171-189, 2007.
DOI : 10.1016/j.ijpe.2006.03.002

. Ellsberg, Risk, ambiguity, and the Savage axioms. Quart, J. Econom, vol.75, pp.643-669, 1961.

T. Gajdos, Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities, Journal of Economic Theory, vol.106, issue.1, pp.190-200, 2002.
DOI : 10.1006/jeth.2001.2851

M. Grabisch, The application of fuzzy integrals in multicriteria decision making, European Journal of Operational Research, vol.89, issue.3, pp.445-456, 1996.
DOI : 10.1016/0377-2217(95)00176-X

M. Grabisch, k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, pp.167-189, 1997.
DOI : 10.1016/s0165-0114(97)00168-1

M. Grabisch and C. Labreuche, Fuzzy measures and integrals in MCDA, Multiple Criteria Decision Analysis, pp.563-608, 2004.
URL : https://hal.archives-ouvertes.fr/halshs-00268985

M. Grabisch, . Ch, and . Labreuche, A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid, pp.1-44, 2008.
URL : https://hal.archives-ouvertes.fr/halshs-00267932

M. Grabisch, J. Duchêne, F. Lino, and P. Perny, Subjective evaluation of discomfort in sitting position. Fuzzy Optimization and Decision Making, pp.287-312, 2002.
URL : https://hal.archives-ouvertes.fr/halshs-00273179

M. Grabisch, . Ch, J. Labreuche, and . Vansnick, On the extension of pseudo-Boolean functions for the aggregation of interacting criteria, European Journal of Operational Research, vol.148, issue.1, pp.28-47, 2003.
DOI : 10.1016/S0377-2217(02)00354-5
URL : https://hal.archives-ouvertes.fr/hal-00272780

C. K. Hsee, The Evaluability Hypothesis: An Explanation for Preference Reversals between Joint and Separate Evaluations of Alternatives, Organizational Behavior and Human Decision Processes, vol.67, issue.3, pp.242-257, 1996.
DOI : 10.1006/obhd.1996.0077

J. Jaffray, Linear utility theory for belief functions, Operations Research Letters, vol.8, issue.2, pp.107-112, 1989.
DOI : 10.1016/0167-6377(89)90010-2

J. Jaffray and P. Wakker, Decision making with belief functions: Compatibility and incompatibility with the sure-thing principle, Journal of Risk and Uncertainty, vol.1, issue.3, pp.255-271, 1993.
DOI : 10.1007/BF01079626

. Ch, M. Labreuche, and . Grabisch, The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets and Systems, pp.11-26, 2003.

T. Marchant, Towards a theory of MCDM: stepping away from social choice theory, Mathematical Social Sciences, vol.45, issue.3, pp.343-363, 2003.
DOI : 10.1016/S0165-4896(02)00069-0

M. Mayag, C. Grabisch, and . Labreuche, A characterization of the 2-additive Choquet integral, Proceedings of IPMU'08 (CD), 2008.
URL : https://hal.archives-ouvertes.fr/halshs-00644232

P. Miranda, M. Grabisch, and P. Gil, p-SYMMETRIC FUZZY MEASURES, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.10, issue.supp01, pp.105-123, 2002.
DOI : 10.1142/S0218488502001867
URL : https://hal.archives-ouvertes.fr/hal-00273960

P. Miranda, M. Grabisch, and P. Gil, Axiomatic structure of k-additive capacities, Mathematical Social Sciences, vol.49, issue.2, pp.153-178, 2005.
DOI : 10.1016/j.mathsocsci.2004.06.001
URL : https://hal.archives-ouvertes.fr/hal-00188165

T. Murofushi and S. Soneda, Techniques for reading fuzzy measures (III): interaction index, 9th Fuzzy System Symposium, pp.693-696, 1993.

E. Pap, Null-Additive Set Functions, Kluwer Academic, 1995.

J. P. Pignon, . Ch, and . Labreuche, A methodological approach for operational and technical experimentation based evaluation of systems of systems architectures, Int. Conference on Software & Systems Engineering and their Applications (ICSSEA), 2007.

D. Schmeidler, Integral representation without additivity, Proc. of the Amer, pp.255-261, 1986.
DOI : 10.1090/S0002-9939-1986-0835875-8

D. Schmeidler, Subjective Probability and Expected Utility without Additivity, Econometrica, vol.57, issue.3, pp.571-587, 1989.
DOI : 10.2307/1911053

G. Shafer, A Mathematical Theory of Evidence, 1976.

L. S. Shapley, A value for n-person games, Contributions to the Theory of Games II, number 28 in Annals of Mathematics Studies, pp.307-317, 1953.

H. Simon, Rational choice and the structure of the environment., Psychological Review, vol.63, issue.2, pp.129-138, 1956.
DOI : 10.1037/h0042769

P. Slovic, M. Finucane, E. Peters, and D. G. Macgregor, The affect heuristic, Heuristics and biases: the psychology of intuitive judgment, pp.397-420, 2002.

. Ph and . Smets, Decision making in the tbm: the necessity of the pignistic transformation, Int. J. Approx. Reasoning, vol.38, issue.2, pp.133-147, 2005.

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, vol.55, issue.1, pp.297-323, 1992.
DOI : 10.1007/BF00122574

V. Neuman and O. Morgenstern, Theory of Games and Economic Behavior, 1944.

. Weber, ???-Decomposable measures and integrals for Archimedean t-conorms ???, Journal of Mathematical Analysis and Applications, vol.101, issue.1, pp.114-138, 1984.
DOI : 10.1016/0022-247X(84)90061-1

J. A. Weymark, Generalized gini inequality indices, Mathematical Social Sciences, vol.1, issue.4, pp.409-430, 1981.
DOI : 10.1016/0165-4896(81)90018-4