×

Generalizing the conjunction rule for aggregating conflicting expert opinions. (English) Zbl 1160.68583

Summary: In multiagent expert systems, the conjunction rule is commonly used to combine expert information represented by imprecise probabilities. However, it is well known that this rule cannot be applied in the case of expert conflict. In this article, we propose to resolve expert conflict by means of a second-order imprecise probability model. The essential idea underlying the model is a notion of behavioral trust. We construct a simple linear programming algorithm for calculating the aggregate. This algorithm explains the proposed aggregation method as a generalized conjunction rule. It also provides an elegant operational interpretation of the imprecise second-order assessments, and thus overcomes the problems of interpretation that are so common in hierarchical uncertainty models.

MSC:

68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence

References:

[1] The elicitation and aggregation of beliefs. Statistics Research Report 23. Technical report, University of Warwick, Coventry; 1982.
[2] Walley, Artif Intell 83 pp 1– (1996)
[3] . Fast Markov chain algorithms for calculating Dempster-Shafer belief. In: Wahlster W, editor. Proc 12th European Conference on Artificial Intelligence. Chichester, U.K.: John Wiley; 1996. pp 672–676.
[4] Walley, Int J Gen Syst 26 pp 337– (1997)
[5] . Aggregation of imprecise probabilities. In: editor. Aggregation and fusion of imperfect information. New York: Physica-Verlag; 1998. pp 162–188. · doi:10.1007/978-3-7908-1889-5_10
[6] De Cooman, J Stat Plann Infer 105 pp 175– (2002)
[7] Nau, J Stat Plann Infer 105 pp 265– (2002)
[8] De Cooman, Theor Decis 52 pp 327– (2002)
[9] Utkin, Uncert Fuzziness Knowl Base Syst 11 pp 301– (2003)
[10] de Cooman, Reliab Eng Syst Saf 85 pp 113– (2004)
[11] Statistical reasoning with imprecise probabilities. London: Chapman and Hall; 1991. · doi:10.1007/978-1-4899-3472-7
[12] de Finetti, Fund Math 17 pp 298– (1931)
[13] Theory of probability: A critical introductory treatment. New York: Wiley; 1974–1975.
[14] The Bayesian choice. New York: Springer; 1994. · doi:10.1007/978-1-4757-4314-2
[15] The enterprise of knowledge. An essay on knowledge, credal probability, and chance. Cambridge, MA: MIT Press; 1983.
[16] Dempster, Ann Math Stat 38 pp 325– (1967)
[17] A mathematical theory of evidence. Princeton, NJ: Princeton University Press; 1976. · Zbl 0359.62002
[18] Zadeh, Fuzzy Sets Syst 1 pp 3– (1978) · Zbl 0377.04002
[19] Choquet, Ann Inst Fourier 5 pp 131– (1953–1954) · Zbl 0064.35101 · doi:10.5802/aif.53
[20] Artzner, Math Finan 9 pp 203– (1999)
[21] Genest, Stat Sci 1 pp 114– (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.