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Two Axiomatic Approaches to Decision Making Using Possibility Theory
Giang, Phan H. Shenoy, Prakash P.
Giang, Phan H.
Shenoy, Prakash P.
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Abstract
This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty, namely, pessimism and optimism. In their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize. We prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility.
Description
A preliminary version of this paper appeared as: "A comparison of axiomatic approaches to qualitative decision making using possibility theory. In J. Breese and D. Koller (eds.), Uncertainty in Artificial Intelligence: Proceedings of the Seventeenth Conference (UAI–
2001), 2001, pp. 162–170, Morgan Kaufmann, San Francisco, CA.
Date
2005-04-16
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Publisher
Elsevier Science Publishers B. V.
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Keywords
Decision theory, Uncertainty, Possibility theory, Utility theory
Citation
European Journal of Operational Research, Vol. 162, No. 2, 2005, pp. 450--467.