Decision Making with Monotone Lower Probabilities of Infinite Order

References

• Buja A. Simultaneously least favorable experiments. Z. Wahrsch. und Verw. Geb. (1984) 65 367 384 Crossref, Google Scholar
• Chateauneuf A. , Jaffray J. Y. Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math. Soc. Sci. (1989) 17 263 283 Crossref, Google Scholar
• Choquet G. Theory of capacities. Ann. Inst. Fourier (1954) 5 131 295 Crossref, Google Scholar
• Choquet G. Forme abstraite du théorème de capacitabilité. Ann. Inst. Fourier (1959) 9 83 89 Crossref, Google Scholar
• Christensen J. P. R. Topology and Borel Structure (1974) (North-Holland, Amsterdam, The Netherlands) Google Scholar
• Cohn D. L. Measure Theory (1980) (Birkhäuser, Boston, MA) Crossref, Google Scholar
• Dellacherie C. Ensembles analytiques, capacités et mesures de Hausdorff (1972) . Lecture Notes in Math. 295, Springer, Berlin, Germany Google Scholar
• Dellacherie C. , Meyer P. A. Probabilités et potentiel (1975) (Hermann, Paris, France) . (Chapter I à IV) Google Scholar
• Dempster A. P. Upper and lower probabilities induced by multivalued mappings. Ann. Math. Statist. (1967) 38 325 335 Crossref, Google Scholar
• Denneberg D. Extensions of a measurable space and linear representation of the Choquet integral. (1995) (Universität Bremen, Germany) . Math. Arbeitspapiere Nr 45 Google Scholar
• Fishburn P. C. Bounded expected utility. Ann. Math. Statist. (1967) 38 1054 1060 Crossref, Google Scholar
• Fishburn P. C. Nonlinear Preference and Utility Theory (1988) (Wheatsheaf, Brighton, UK) Google Scholar
• Gilboa I. Expected utility with purely subjective nonadditive probabilities. J. Math. Econom. (1987) 16 65 88 Crossref, Google Scholar
• Gilboa I. , Schmeidler D. Maxmin expected utility with a nonunique prior. J. Math. Econom. (1989) 18 141 153 Crossref, Google Scholar
• Gilboa I. , Schmeidler D. Canonical representation of set functions. Math. Oper. Res. (1995) 20 197 212 Link, Google Scholar
• Hendon E. , Jacobsen H. J. , Sloth B. , Tranaes T. Expected utility with lower probabilities. J. Risk and Uncertainty (1993) 8 197 216 Crossref, Google Scholar
• Herstein I. N. , Milnor J. An axiomatic approach to measurable utility. Econometrica (1953) 21 291 297 Crossref, Google Scholar
• Huber P. J. , Strassen V. Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. (1973) 1 251 263 Crossref, Google Scholar
• Jaffray J. Y. Généralisation du critère de l'utilité espérée aux choix dans l'incertain régulier. RAIRO (1989a) 23 237 267 Google Scholar
• Jaffray J. Y. Linear utility theory and belief functions. Oper. Res. Lett. (1989b) 8 107 112 Crossref, Google Scholar
• Jaffray J. Y. , Chikan A. Linear utility theory and belief functions: A discussion. Proc. FUR IV Conf. (1991) (Kluwer, Dordrecht, The Netherlands) Google Scholar
• Jaffray J. Y. , Philippe F. On the existence of subjective upper and lower probabilities. Math. Oper. Res. (1997) 22 165 185 Link, Google Scholar
• Jensen N. E. An introduction to Bernoullian utility theory: I: Utility functions. Swedish J. Econom. (1967) 69 163 183 Crossref, Google Scholar
• Marinacci M. Decomposition and representation of coalitional games. Math. Oper. Res. (1996) 21 1000 1015 Link, Google Scholar
• Matheron G. Random Sets and Integral Geometry (1975) (Wiley, New York) Google Scholar
• Meyer P. A. Probabilités et Potentiel (1966) (Hermann, Paris, France) Google Scholar
• Nguyen H. T. On random sets and belief functions. J. Math. Anal. Appl. (1978) 65 531 542 Crossref, Google Scholar
• Parthasarathy K. R. Probability Measures on Metric Spaces (1967) (Academic Press, New York) Crossref, Google Scholar
• Rota G. C. Theory of Mäbius functions. Z. Wahrsch. und Verw. Geb. (1964) 2 340 368 Crossref, Google Scholar
• Schmeidler D. Subjective probability and expected utility without additivity. Econometrica (1989) 57 571 587 Crossref, Google Scholar
• Shafer G. A Mathematical Theory of Evidence (1976) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Shapley L. S. A value for n-person games. Ann. Math. Stud. (1953) 28 307 317 Google Scholar
• Shapley L. S. Cores of convex games. Internat. J. Game Theory (1971) 1 11 26 Crossref, Google Scholar
• Sion M. On general minimax theorems. Pacific J. Math. (1958) 8 171 176 Crossref, Google Scholar
• Strassen V. Messfehler und information. Z. Wahrsch. und Verw. Geb. (1964) 2 273 305 Crossref, Google Scholar
• Wakker P. P. Additive Representations of Preferences (1989) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Walley P. Statistical Reasoning with Imprecise Probabilities (1991) (Chapman and Hall, London, UK) Crossref, Google Scholar
• Wasserman L. A. , Kadane J. B. Bayes' theorem for Choquet capacities. Ann. Statist. (1990) 18 1328 1339 Crossref, Google Scholar