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Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion

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Cited by:

  1. Pedro Miranda & Michel Grabisch, 2012. "An algorithm for finding the vertices of the k-additive monotone core," Post-Print hal-00806905, HAL.
  2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Post-Print halshs-00445132, HAL.
  3. Grabisch, Michel & Li, Tong, 2011. "On the set of imputations induced by the k-additive core," European Journal of Operational Research, Elsevier, vol. 214(3), pages 697-702, November.
  4. Lehrer, Ehud, 2005. "Updating non-additive probabilities-- a geometric approach," Games and Economic Behavior, Elsevier, vol. 50(1), pages 42-57, January.
  5. Kolesárová, Anna & Li, Jun & Mesiar, Radko, 2018. "k-additive aggregation functions and their characterization," European Journal of Operational Research, Elsevier, vol. 265(3), pages 985-992.
  6. Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2018. "Infinite Supermodularity and Preferences," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
  7. Grabisch, Michel & Labreuche, Christophe, 2018. "Monotone decomposition of 2-additive Generalized Additive Independence models," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 64-73.
  8. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
  9. Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006. "Dominance of capacities by k-additive belief functions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 912-930, December.
  10. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.
  11. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
  12. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
  13. Jean-Yves Jaffray & Philippe Mongin, 2003. "Constrained egalitarianism in a simple redistributive model," Theory and Decision, Springer, vol. 54(1), pages 33-56, February.
  14. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
  15. Miranda, Pedro & Grabisch, Michel, 2010. "k-Balanced games and capacities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 465-472, January.
  16. repec:hal:pseose:hal-00803233 is not listed on IDEAS
  17. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
  18. Jian-Zhang Wu & Yi-Ping Zhou & Li Huang & Jun-Jie Dong, 2019. "Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
  19. Michel Grabisch, 2015. "Bases and transforms of set functions," Post-Print halshs-01169287, HAL.
  20. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
  21. Pereira, Miguel Alves & Figueira, José Rui & Marques, Rui Cunha, 2020. "Using a Choquet integral-based approach for incorporating decision-maker’s preference judgments in a Data Envelopment Analysis model," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1016-1030.
  22. Sebastian Maaß, 2006. "A Philosophical Foundation of Non-Additive Measure and Probability," Theory and Decision, Springer, vol. 60(2), pages 175-191, May.
  23. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.
  24. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray July 22, 1939 - February 26, 2009," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00664715, HAL.
  25. Klaus Nehring, 2003. "Preference for Flexibility and Freedom of Choice in a Savage Framework," Working Papers 51, University of California, Davis, Department of Economics.
  26. Mikhail Timonin, 2012. "Maximization of the Choquet integral over a convex set and its application to resource allocation problems," Annals of Operations Research, Springer, vol. 196(1), pages 543-579, July.
  27. Miranda, P. & Combarro, E.F. & Gil, P., 2006. "Extreme points of some families of non-additive measures," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1865-1884, November.
  28. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print hal-00272084, HAL.
  29. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
  30. Miranda, P. & Grabisch, M. & Gil, P., 2005. "Axiomatic structure of k-additive capacities," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 153-178, March.
  31. Fabien Lange & Michel Grabisch, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
  32. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray," Theory and Decision, Springer, vol. 71(1), pages 1-10, July.
  33. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
  34. Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.
  35. Giulianella Coletti & Davide Petturiti & Barbara Vantaggi, 2019. "Dutch book rationality conditions for conditional preferences under ambiguity," Annals of Operations Research, Springer, vol. 279(1), pages 115-150, August.
  36. Victor H. Aguiar & Maria Jose Boccardi & Nail Kashaev & Jeongbin Kim, 2023. "Random utility and limited consideration," Quantitative Economics, Econometric Society, vol. 14(1), pages 71-116, January.
  37. Rigotti, L. & Ryan, M. & Vaithianathan, R., 2001. "Entrepreneurial Innovation," Discussion Paper 2001-21, Tilburg University, Center for Economic Research.
  38. Dominiak, Adam & Eichberger, Jürgen, 2016. "Support notions for belief functions," Economics Letters, Elsevier, vol. 146(C), pages 28-32.
  39. Daniel Li Li & Erfang Shan, 2020. "Marginal contributions and derivatives for set functions in cooperative games," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 849-858, April.
  40. Matthew Ryan, 2019. "Generalised Random Categorisation Rules," Working Papers 2019-03, Auckland University of Technology, Department of Economics.
  41. Silvia Angilella & Sally Giuseppe Arcidiacono & Salvatore Corrente & Salvatore Greco & Benedetto Matarazzo, 2020. "An application of the SMAA–Choquet method to evaluate the performance of sailboats in offshore regattas," Operational Research, Springer, vol. 20(2), pages 771-793, June.
  42. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
  43. Luca Rigotti & Matthew Ryan & Rhema Vaithianathan, 2016. "Throwing good money after bad," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 175-202, November.
  44. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
  45. Aguiar, Victor H., 2017. "Random categorization and bounded rationality," Economics Letters, Elsevier, vol. 159(C), pages 46-52.
  46. Luca Rigotti & Matthew Ryan & Rhema Vaithianathan, 2011. "Optimism and firm formation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 1-38, January.
  47. Alain Chateauneuf & Thibault Gajdos & Jean-Yves Jaffray, 2011. "Regular updating," Theory and Decision, Springer, vol. 71(1), pages 111-128, July.
  48. Kojadinovic, Ivan, 2004. "Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals," European Journal of Operational Research, Elsevier, vol. 155(3), pages 741-751, June.
  49. Torra, Vicenç, 2023. "The transport problem for non-additive measures," European Journal of Operational Research, Elsevier, vol. 311(2), pages 679-689.
  50. Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January.
  51. Bouyssou, Denis & Marchant, Thierry, 2013. "Multiattribute preference models with reference points," European Journal of Operational Research, Elsevier, vol. 229(2), pages 470-481.
  52. Abellán, Joaquín & Baker, Rebecca M. & Coolen, Frank P.A., 2011. "Maximising entropy on the nonparametric predictive inference model for multinomial data," European Journal of Operational Research, Elsevier, vol. 212(1), pages 112-122, July.
  53. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
  54. Mikhail Timonin, 2016. "Choquet integral in decision analysis - lessons from the axiomatization," Papers 1611.09926, arXiv.org.
  55. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
  56. Hamed Hamze Bajgiran & Federico Echenique, 2022. "Closure operators: Complexity and applications to classification and decision-making," Papers 2202.05339, arXiv.org, revised May 2022.
  57. Lopomo, Giuseppe & Rigotti, Luca & Shannon, Chris, 2011. "Knightian uncertainty and moral hazard," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1148-1172, May.
  58. Takao Asano & Hiroyuki Kojima, 2013. "Modularity and Monotonicity of Games," KIER Working Papers 871, Kyoto University, Institute of Economic Research.
  59. Michael Magill & Klaus Nehring & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 263, University of California, Davis, Department of Economics.
  60. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
  61. Vassili Vergopoulos, 2011. "Dynamic consistency for non-expected utility preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 493-518, October.
  62. Yaron Azrieli & John Rehbeck, 2022. "Marginal stochastic choice," Papers 2208.08492, arXiv.org.
  63. Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
  64. Angilella, Silvia & Greco, Salvatore & Lamantia, Fabio & Matarazzo, Benedetto, 2004. "Assessing non-additive utility for multicriteria decision aid," European Journal of Operational Research, Elsevier, vol. 158(3), pages 734-744, November.
  65. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
  66. Keiran Sharpe, 2018. "On Risk and Uncertainty, and Objective versus Subjective Probability," The Economic Record, The Economic Society of Australia, vol. 94(S1), pages 49-72, June.
  67. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
  68. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
  69. Patrick Meyer & Grégory Ponthière, 2011. "Eliciting Preferences on Multiattribute Societies with a Choquet Integral," Computational Economics, Springer;Society for Computational Economics, vol. 37(2), pages 133-168, February.
  70. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
  71. Michel Grabisch, 2006. "Capacities and Games on Lattices: A Survey of Result," Post-Print halshs-00179830, HAL.
  72. Silvia Bortot & Ricardo Alberto Marques Pereira, 2013. "The binomial Gini inequality indices and the binomial decomposition of welfare functions," Working Papers 305, ECINEQ, Society for the Study of Economic Inequality.
  73. Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
  74. Takao Asano & Hiroyuki Kojima, 2014. "Modularity and monotonicity of games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 29-46, August.
  75. Chateauneuf, Alain, 1996. "Decomposable capacities, distorted probabilities and concave capacities," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 19-37, February.
  76. Gianluca Cassese, 2020. "Semilattices, canonical embeddings and representing measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 55-74, June.
  77. Ben Abdelaziz, F. & Masri, H., 2005. "Stochastic programming with fuzzy linear partial information on probability distribution," European Journal of Operational Research, Elsevier, vol. 162(3), pages 619-629, May.
  78. Bernt P. Stigum, 2000. "Rationality in Econometrics," Econometric Society World Congress 2000 Contributed Papers 0747, Econometric Society.
  79. Satoshi Masuya & Masahiro Inuiguchi, 2016. "A fundamental study for partially defined cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 281-306, September.
  80. Takao Asano & Hiroyuki Kojima & Kaname Miyagishima, 2022. "A Simple Axiomatization of Neo-Additive Choquet Expected Utility Theory on a Finite State Space," KIER Working Papers 1080, Kyoto University, Institute of Economic Research.
  81. Nehring, Klaus & Puppe, Clemens, 2004. "Modelling cost complementarities in terms of joint production," Journal of Economic Theory, Elsevier, vol. 118(2), pages 252-264, October.
  82. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
  83. Eichberger, Jürgen & Pasichnichenko, Illia, 2021. "Decision-making with partial information," Journal of Economic Theory, Elsevier, vol. 198(C).
  84. Andrea Cinfrignini & Davide Petturiti & Barbara Vantaggi, 2023. "Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting," Annals of Operations Research, Springer, vol. 321(1), pages 103-137, February.
  85. Takao Asano & Hiroyuki Kojima, 2015. "An axiomatization of Choquet expected utility with cominimum independence," Theory and Decision, Springer, vol. 78(1), pages 117-139, January.
  86. Victor Ivanenko & Illia Pasichnichenko, 2019. "Kolmogorov Consistency Theorem for Nonstochastic Random Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 399-405, December.
  87. Branke, Juergen & Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman & Zielniewicz, Piotr, 2016. "Using Choquet integral as preference model in interactive evolutionary multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 884-901.
  88. Takao Asano & Hiroyuki Kojima, 2013. "An Axiomatization of Choquet Expected Utility with Cominimum Independence," KIER Working Papers 878, Kyoto University, Institute of Economic Research.
  89. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.
  90. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
  91. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
  92. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
  93. repec:hal:pseose:halshs-01235625 is not listed on IDEAS
  94. Fabrice Philippe & Gabriel Debs & Jean-Yves Jaffray, 1999. "Decision Making with Monotone Lower Probabilities of Infinite Order," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 767-784, August.
  95. Silvia Angilella & Marta Bottero & Salvatore Corrente & Valentina Ferretti & Salvatore Greco & Isabella M. Lami, 2016. "Non Additive Robust Ordinal Regression for urban and territorial planning: an application for siting an urban waste landfill," Annals of Operations Research, Springer, vol. 245(1), pages 427-456, October.
  96. Angilella, Silvia & Greco, Salvatore & Matarazzo, Benedetto, 2010. "Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral," European Journal of Operational Research, Elsevier, vol. 201(1), pages 277-288, February.
  97. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
  98. Marichal, Jean-Luc, 2004. "Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral," European Journal of Operational Research, Elsevier, vol. 155(3), pages 771-791, June.
  99. F. Beaudouin, 2015. "Implementing a Multiple Criteria Model to Debate About Nuclear Power Plants Safety Choices," Group Decision and Negotiation, Springer, vol. 24(6), pages 1035-1063, November.
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