A New Approach on ρ to Decision Making Using Belief Functions Under Incomplete Information
This paper discusses an expected utility approach on ρ to decision making under incomplete information using the belief function framework. In order to make rational decisions under incomplete information, some subjective assumptions often need to be made because of the interval representations of the belief functions. We assume that a decision maker may have some evidence from different sources about the value of ρ, and this evidence can also be represented by a belief function or can result in a unique consonant belief function that is constrained by the evidence over the same frame of discernment. We thus propose a novel approach based on the two-level reasoning Transferable Belief Model and calculate the expected utility value of ρ using pignistic probabilities transformed from the interval-based belief functions. The result can then be used to make a choice between overlapped expected value intervals. Our assumption is between the strongest assumption of a warranted point value of ρ and the weakest assumption of a uniform probability distribution for an unwarranted ρ.
KeywordsHide Sector Belief Function Credal Level Focal Element Basic Probability Assignment
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- 4.Clemen, R.T., Winkler, R.L.: Combining Probability Distributions From Experts in Risk Analysis. Risk Analysis 19(2), 187–203 (1999)Google Scholar
- 5.Lesh, S.A.: An evidential theory approach to judgement-based decision making, PhD thesis, Dept. of Forestry and Environmental Studies, Duke University (1986)Google Scholar
- 6.Strat, T.M.: Decision Analysis Using Belief Functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence. John Wiley and Sons, New York (1994)Google Scholar
- 7.Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Process, pp. 167–181. North-Holland, Amsterdam (1982)Google Scholar
- 8.Nguyen, H.T., Walker, E.A.: On Decision Making Using Belief Functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence. John Wiley and Sons, New York (1994)Google Scholar
- 11.Smets, P.: Decision Making in a Context where Uncertainty is Represented by Belief Functions. In: Srivastava, R., Mock, T.J. (eds.) Belief Functions in Business Decisions, pp. 17–61. Physica-Verlag, Heidelberg (2002)Google Scholar
- 13.Dubois, D., Prade, H.: The principle of minimum specificity as a basis for evidential reasoning. In: IPMU, pp. 75–84 (1986)Google Scholar
- 14.Dubois, D., Prade, H., Smets, P.: New semantics for quantitative possibility theory. In: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, Ithaca, NY, USA, pp. 152–161 (2001)Google Scholar
- 15.Smets, P.: Probability, Possibility, Belief: Which and Where. In: Gabbay, D., Smets, P., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Quantified Representation of Uncertainty and Imprecision, vol. 1, pp. 1–24. Kluwer, Doordrecht (1998)Google Scholar