Summary
The paper discusses betting on sport events by a fuzzy-rational decision maker, who elicits interval subjective probabilities, which may be conveniently described by intuitionistic fuzzy sets. Finding the optimal bet for this decision maker is modeled and solved using fuzzy-rational generalized lotteries of II type. Approximation of interval probabilities is performed with the use of four criteria under strict uncertainty. Four expected utility criteria are formulated on that basis. The scheme accounts for the interval character of probability elicitation results. Index Terms. – generalized lotteries of II type, intuitionistic fuzzy sets, fuzzy rationality, interval probabilities.
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References
Alvarez DA (2006) On the calculation of the bounds of probability of events using infinite random sets, International Journal of Approximate Reasoning 43: 241–267
Atanassov K (1999) Intuitionistic fuzzy sets. Berlin Heidelberg New York: Springer
Atanassov K (2002) Elements of intuitionistic fuzzy logics. Part II: Intuitionistic fuzzy modal logics. Advanced Studies on Contemporary Mathematics, 5(1): 1–13.
Augustin Th (2001) On decision making under ambiguous prior and sampling information. In: de Cooman G, Fine T, Moral S, Seidenfeld T. (eds.): ISIPTA ‘01: Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications. Cornell University, Ithaca (N.Y.), Shaker, Maastricht, 9–16
Augustin Th (2005) Generalized basic probability assignments. International Journal of General Systems, 34(4): 451–463
Bernstein L (1996) Against the gods – the remarkable story of risk. Wiley, USA
De Finetti B (1937) La prevision: ses lois logiques, ses sorces subjectives. In: Annales de l’Institut Henri Poincare, 7: 1–68. Translated in Kyburg HE Jr., Smokler HE (eds.) (1964) Studies in subjective probability. Wiley, New York, 93–158
De Groot MH (1970) Optimal statistical decisions. McGraw-Hill
Fine TL (1973) Theories of probability. Academic Press
Forsythe GE, Malcolm A, Moler CB (1977) Computer methods for mathematical computations. Prentice Hall
French S. (1993) Decision theory: an introduction to the mathematics of rationality. Ellis Horwood.
French S, Insua DR (2000) Statistical decision theory. Arnold, London
Gatev G (1995) Interval analysis approach and algorithms for solving network and dynamic programming problems under parametric uncertainty. Proc. of the Technical University-Sofia, 48(4): 343–350, Electronics, Communication, Informatics, Automatics
Gould NIM, Leyffer S (2003) An introduction to algorithms for nonlinear optimization. In Blowey JF, Craig AW, Shardlow, Frontiers in numerical analysis. Springer, Berlin Heidelberg New York, 109–197
Grunwald PD, Dawid AP (2002) Game theory, maximum entropy, minimum discrepancy, and robust bayesian decision theory. Tech. Rep. 223, University College London
Levi I (1999) Imprecise and indeterminate probabilities. Proc. First International Symposium on Imprecise Probabilities and Their Applications, University of Ghent, Ghent, Belgium, 65–74.
Machina M, Schmeidler D (1992) A more rrobust definition of subjective probability. Econometrica, 60(4): 745–780
Moore R (1979) Methods and applications of interval analysis. SIAM, Philadelphia
von Neumann J, Morgenstern O (1947) Theory of games and economic behavior. Second Edition. Princeton University Press, Princeton, NJ
Nikolova ND (2006) Two criteria to rank fuzzy rational alternatives. Proc. International Conference on Automatics and Informatics, 3–6 October, Sofia, Bulgaria, 283–286
Nikolova ND (2007) Quantitative fuzzy-rational decision analysis, PhD Dissertation, Technical University-Varna (in Bulgarian)
Nikolova ND, Dimitrakiev D, Tenekedjiev K (2004) Fuzzy rationality in the elicitation of subjective probabilities. Proc. Second International IEEE Conference on Intelligent Systems IS’2004, Varna, Bulgaria, III: 27–31
Nikolova ND, Shulus A, Toneva D, Tenekedjiev K (2005) Fuzzy rationality in quantitative decision analysis. Journal of Advanced Computational Intelligence and Intelligent Informatics, 9(1): 65–69
Press WH, Teukolski SA, Vetterling WT, Flannery BP (1992) Numerical recipes – the art of scientific computing, Cambridge University Press
Raiffa H (1968) Decision analysis. Addison Wesley
Satia JK, Lave RE, Lave Jr (1973) Markovian decision processes with uncertain transition probabilities. Operations Research, 21(3): 728–740
Schervish M, Seidenfeld T, Kadane J, Levi JI (2003) Extensions of expected utility theory and some limitations of pairwise comparisons. In Bernard JM, Seidenfeld T, Zaffalon M (eds.): ISIPTA 03: Proc. of the Third International Symposium on Imprecise Probabilities and their Applications, Lugano. Carleton Scientific, Waterloo, 496–510.
Shafer G, Gillett P, Scherl R (2003) A new understanding of subjective probability and its generalization to lower and upper prevision. International Journal of Approximate Reasoning, (33): 1–49
Szmidt E, Kacprzyk J (1999) Probability of intuitionistic fuzzy events and their application in decision making, Proc. EUSFLAT-ESTYLF Joint Conference, September 22–25, Palma de Majorka, Spain, 457–460
Tenekedjiev K (2006) Hurwiczα expected utility criterion for decisions with partially quantified uncertainty, In First International Workshop on Intuitionistic Fuzzy Sets, Generalized Nets and Knowledge Engineering, 2–4 September, London, UK, 2006, pp. 56–75.
Tenekedjiev K (2007) Triple bisection algorithms for 1-D utility elicitation in the case of monotonic preferences. Advanced Studies in Contemporary Mathematics, 14(2): 259–281.
Tenekedjiev K, Nikolova ND (2007) Ranking discrete outcome alternatives with partially quantified uncertainty. International Journal of General Systems, 37(2): 249–274
Tenekedjiev K, Nikolova ND, Kobashikawa C, Hirota K (2006) Conservative betting on sport games with intuitionistic fuzzy described uncertainty. Proc. Third International IEEE Conference on Intelligent Systems IS’2006, Westminster, UK, 747–754
The MathWorks (2007) MATLAB optimization toolbox 3 – user’s guide. The MathWorks Inc.
Vidakovic B (2000) Γ-minimax: a paradigm for conservative robust Bayesians. In Insua DR, Ruggeri F (eds.) Robust bayesian analysis, 241–259
Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, London.
Zaffalon M, Wesnes K, Petrini O (2003) Reliable diagnoses of dementia by the naive credal classifier inferred from incomplete cognitive data, Artificial Intelligence in Medicine, 29(1–2): 61–79
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Tenekedjiev, K.I., Nikolova, N.D., Kobashikawa, C.A., Hirota, K. (2008). Fuzzy-Rational Betting on Sport Games with Interval Probabilities. In: Chountas, P., Petrounias, I., Kacprzyk, J. (eds) Intelligent Techniques and Tools for Novel System Architectures. Studies in Computational Intelligence, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77623-9_25
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DOI: https://doi.org/10.1007/978-3-540-77623-9_25
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