Abstract
A qualitative counterpart to Von Neumann and Morgenstern's Expected Utility Theory of decision under uncertainty was recently proposed by Dubois and Prade. In this model, belief states are represented by normalised possibility distributions over an ordinal scale of plausibility, and the utility (or preference) of consequences of decisions are also measured in an ordinal scale. In this paper we extend the original Dubois and Prade's decision model to cope with partially inconsistent descriptions of belief states, represented by non-normalised possibility distributions. Subnormal possibility distributions frequently arise when adopting the possibilistic model for case-based decision problems. We consider two qualitative utility functions, formally similar to the original ones up to modifying factors coping with the inconsistency degree of belief states. We provide axiomatic characterizations of the preference orderings induced by these utility functions.
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References
J. von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour, Princeton Univ. Press: Princeton, NJ, 1944.
A. Zapico and L. Godo, "On the possibilistic-based decision model: Preferences under partially inconsistent belief states," in Proc of the Workshop on Decision Theory Meets Artificial Intelligence: Qualitative and Quantitative Approaches. ECAI'98. Brighton 1998, pp. 99-109.
D. Schmeidler, "Subjective probability and expected utility without additivity," in Econometrica, vol. 57, pp. 571-587, 1989.
I. Gilboa, "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, vol.16, pp. 65-88, 1987.
R. Sarin and P.P. Wakker, "A simple axiomatization of nonadditive expected utility," Econometrica, vol. 60, no 6, pp. 1255-1272, 1992.
R.R. Yager, "Possibilistic decision making," IEEE Trans. on Systems, Man and Cybernetics, vol. 9, pp. 388-392, 1979.
J. Doyle and R. Thomason, "Background to qualitative decision theory". AI Magazine, vol. 20, no. 2, pp. 55-68, 1999.
B. Bonet and H. Geffner, "Arguing for decisions: A qualitative model of decision making," in Proc. of the 12th Conf. on Uncertainty in Artificial Intelligence, Portland, OR, edited by E. Horwitz and F. Jensen, pp. 98-105, 1996.
R.I. Brafman and M. Tennenholtz, "On the axiomatization of qualitative decision criteria," in Proc. 14th Nat. Conf. on A.I. (AAI'97), 1997, pp. 76-81.
J. Pearl, "From qualitative utility to conditional"ought to"," in Proc. of the 9th Inter. Conf. on Uncertainty in Artificial Intelligence, edited by D. Heckerman, H. Mamdani, pp. 12-20, 1993.
D. Dubois and H. Prade, "A fuzzy set approach to case based decision," in Proc. of the Second European Workshop on Fuzzy Decision Analysis and Neural networks for Management, Planning and Optimization (EFDAN97), Dortmund, 1997, pp. 1-9.
D. Dubois, L. Godo, H. Prade, and A. Zapico, "Making decision in a qualitative setting: From decision under uncertainty to case based decision," in Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR'98). Trento, 1998, pp. 594-605.
I. Gilboa and D. Schmeidler, "Case-based decision theory," The Quarterly Journal of Economics, vol. 110, pp. 607-639, 1995.
D. dubois and Prade H. "Possibility theory as a basis for qulitative decision theory," in Proc. of the 14th Int. Joint Conf. on Artificial Intellignce (IJCAI '95), Montreal, 1995, pp. 1924-1930.
T. Whalen, "Decision making under uncertainty with various assumptions about available information." IEEE Trans. on Systems, Man and Cybernetics, vol. 14, pp. 888-900, 1984.
D. Dubois, J.C. Fodor, H. Prade, and M. Roubens "Aggregation of decomposable measures with application to utility theory," in Theory and Decision, vol. 41, pp. 59-95, 1996.
D. Dubois, F. Esteva, P. Garcia, L. Godo, R.L. de Màntaras, and H. Prade, "Fuzzy set modelling in case-based reasoning," International Journal of Intelligent Systems, vol. 13, pp. 345-373, 1998.
D. Dubois, H. Lang, and H. Prade, "Possibilistic logic," Handbook of Logic in Artificial Intelligence and Logic Programming, edited by D.M. Gabbay, C.J. Hopper, J.A. Robinson, Oxford University Press, Oxford, UK, vol. 3, pp. 439-513, 1994.
A. Zapico, "Axiomatic foundations for qualitative/ordinal decisions with partial preferences," in Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI'99), Stockholm, 1999, pp. 132-137.
L. Godo and A. Zapico, "Generalised qualitative utility functions for representing partial preference relations," Proc. of EUSFLAT'99, Palma de Mallorca, Sept. 22-25, Spain, 1999, pp. 343-346.
C. Boutilier, "Toward a logic for qualitative decision theory," in Proc. 4th. Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR'94), Bonn, 1994, pp. 75-86.
L.J. Savage, The Foundations of Statistics. Dover: New York.
D. Schmeidler, "Integral representation without additivity", in Proc. Amer. Math. Soc., vol. 9, 1986, pp. 255-261.
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Godo, L., Zapico, A. On the Possibilistic-Based Decision Model: Characterization of Preference Relations Under Partial Inconsistency. Applied Intelligence 14, 319–333 (2001). https://doi.org/10.1023/A:1011203021670
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DOI: https://doi.org/10.1023/A:1011203021670