Title of paper:
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FUZZY-RATIONAL EXPLANATION OF THE ELLSBERG PARADOX
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Author(s):
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Kiril Tenekedjiev
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Technical University – Varna, 1 Studentska Str., 9010 Varna, Bulgaria
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kiril@dilogos.com
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Published in:
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"Notes on IFS", Volume 12 (2006) Number 2, pages 39-52
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Download:
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PDF (233 Kb, File info)
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Abstract:
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The paper analyses the Ellsberg paradox from the point of view of fuzzy rational decision makers, who can only partially measure uncertainty in terms of interval probabilities. Alternatives are modeled as fuzzy-rational lotteries, and are brought down to classical risky lotteries using intuitionistic operators according to a preliminarily chosen decision criterion under strict uncertainty. The Hurwicz α expected utility criterion serves to prove that declared preferences in the Ellsberg paradox are consistent and reasonable, if the fuzzyrational decision maker is a moderate or extreme pessimist.
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Keywords:
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Ellsberg paradox, ambiguity, fuzzy rationality, partially quantified uncertainty, interval probabilities, Hurwicz α expected utility
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AMS Classification:
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03E72
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References:
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- Atanassov, K., Review and New Results on Intuitonistic Fuzzy Sets, Preprint IM-MFAIS, Volume 1-88, Sofia, 1988.
- Atanassov, K., Four New Operators on Intuitionistic Fuzzy Sets, Preprint IM-MFAIS, Volume 4-89, Sofia, 1989
- Atanassov, K., Intuitionistic Fuzzy Sets, Springer-Verlag, Heidelberg, 1999.
- Ben-Haim, Y., Info-Gap Decision Theory: Decisions Under Severe Uncertainty, Second Edition, Academic Press, London, 2006.
- Bernstein, P. L. Against the Gods – the Remarkable Story of Risk, John Wiley, 1996.
- Chew, S.H., A Generalization of the Quasilinear Mean with Applications to the Measurement of Inequality and the Decision Theory Resolving the Allais Paradox, Econometrica, 51, 1065-1092, 1983
- Clemen, R., Making Hard Decisions: an Introduction to Decision Analysis, Second Edition, Duxbury Press, Wadsworth Publishing Company, 1996.
- Cohen, M., J.Y. Jaffray, T. Said, Individual Behavior Under Risk and Uncertainty: an Experimental Study, Theory and Decision, 18, 203-228, 1985
- De Groot, M. H., Optimal Statistical Decisions, McGraw-Hill, 1970.
- Ellsberg, D., Risk Ambiguity and Savage Axioms, Quarterly Journal of Economics, 75, 643–699, 1961.
- Fox, C. R., A. Tversky, Ambiguity Aversion and Comparative Ignorance, Quarterly Journal of Economics, CX, No 3, 585–603, 1995.
- French, S., Decision Theory: an Introduction to the Mathematics of Rationality, Ellis Horwood, 1993.
- French, S., D. R. Insua, Statistical Decision Theory, Arnold, 2000.
- Hurwicz, L., Optimality criteria for decision making under ignorance, Cowles Commission Discussion Paper No. 370 (mimeographed), 1951.
- Kahneman, D., A. Tversky, On the Psychology of Predictions, Psychological Review, 80, 237–251, 1973.
- Kahneman, D., A. Tversky, Prospect Theory: an Analysis of Decision Under Risk, Econometrica, 47, 263–291, 1979.
- Keeney, R. L., H. Raiffa, Decisions with Multiple Objectives: Preference and Value Tradeoffs, Cambridge University Press, 1993.
- Maccrimon, K. R., S. Larsson, Utility Theory: Axioms Versus “Paradoxes”, In: Allais, M., J. Hagen, Expected Utility Hypotheses and the Allias Paradox, Dortrecht, The Netherlands: Reidel, 191–243, 1979.
- Machina, M.J., Expected Utility Analysis Without the Independence Axiom, Econometrica, 51, 277-323, 1982.
- Nikolova, N., Two criteria to rank fuzzy rational lotteries, Proc. Automatics and Informatics, Sofia, Bulgaria, 4, 41-48, 2006.
- Nikolova, N.D., A. Shulus, D. Toneva, K. Tenekedjiev, Fuzzy Rationality in Quantitative Decision Analysis, Journal of Advanced Computational Intelligence and Intelligent Informatics, vol. 9, No. 1, pp. 65-69, 2005.
- Pratt, J. W., H. Raiffa, R. Schlaifer, Introduction to Statistical Decision Theory, Cambridge, Massachusetts: MIT Press, 1995.
- Press, W. H., S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes – the Art of Scientific Computing, Cambridge University Press, 1992.
- Quiggin, J., Generalized Expected Utility Theory, the Rank-Dependent Model, Boston: Kluwer Academic Publishers, 1993.
- Ramsay, F. P., Truth and Probability. The Logical Foundations of Mathematics and Other Essays, Kegan Paul (reprint in Kyburg, H.E. Jr., Smolker, H.E., Studies in subjective probability (eds), 61-92, John Wiley, 1964), 1931.
- Rapoport, Decision Theory and Decision Behaviour - Normative and Descriptive Approaches, Kluwer Academic Publishers, 1989.
- Savage, L.J., The theory of statistical decision, J Amer Statist Assoc, 46, 55-67, 1951.
- Savage, L. J., The Foundations of Statistics, First Edition, John Wiley, 1954.
- Segal, U., The Ellsberg Paradox and Risk Aversion: an Anticipated Utility Approach, International Economic Review, 28, 175-202, 1987
- Slovic, P., A. Tversky, Who Accepts Savage’s Axiom, Behavioral Science, 19, 368-373, 1974
- Tenekedjiev, K., Quantitative Decision Analysis – Utility Theory and Subjective Statistics, Marin Drinov Academic Publishing House, Sofia, Bulgaria, 2004.
- Tenekedjiev, K, Hurwicz- αExpected Utility Criterion for Decisions with Partially Quantified Uncertainty, Proc. First International Workshop on Intuitionistic Fuzzy Sets, Generalized Nets and Knowledge Engineering, 56-75, University of Westminster, London, UK, 2006.
- Tenekedjiev, K., Nikolova, N.D., Dimitrakiev, D., Application of the Triple Bisection Method for Extraction of Subjective Utility Information, Proc. Second International Conference "Management and Engineering’2004", vol. 2(70), pp. 115-117, Sofia, Bulgaria, 2004.
- Tversky, A., D. Kahneman, Judgment under Uncertainty: Heuristics and Biases, Science, 185, 1124–1131, 1974.
- Villigas, C., On Qualitative Probability σ -Algebras, Ann. Math. Statis., 35, 1787–1796, 1964.
- Von Neumann, J., O. Morgenstern, Theory of Games and Economic Behavior, Second Edition, Princeton University Press, 1947.
- Wald, А., Statistical Decision Functions, John Wiley, 1950.
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