A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory
arXiv:1301.2271
Abstract
In this paper we analyze two recent axiomatic approaches proposed by Dubois et al and by Giang and Shenoy to qualitative decision making where uncertainty is described by possibility theory. Both axiomtizations are inspired by von Neumann and Morgenstern's system of axioms for the case of probability theory. We show that our approach naturally unifies two axiomatic systems that correspond respectively to pessimistic and optimistic decision criteria proposed by Dubois et al. The simplifying unification is achieved by (i) replacing axioms that are supposed to reflect two informational attitudes (uncertainty aversion and uncertainty attraction) by an axiom that imposes order on set of standard lotteries and (ii) using a binary utility scale in which each utility level is represented by a pair of numbers.
Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001)
References in corpus (1)
Cited by in corpus (6)
- Statistical Decisions Using Likelihood Information Without Prior Probabilities
- Axiomatic Foundations for a Class of Generalized Expected Utility: Algebraic Expected Utility
- On the Complexity of Decision Making in Possibilistic Decision Trees
- Great Expectations. Part II: Generalized Expected Utility as a Universal Decision Rule
- Qualitative Decision Making Under Possibilistic Uncertainty: Toward more discriminating criteria
- Decision Making for Symbolic Probability