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A framework for analysing decisions under risk. (English) Zbl 0960.91505

Summary: The main objective is to present a framework for analysing decisions under risk. The nature of much information available to decision makers is vague and imprecise, be it information for human managers in organisations or for process agents in a distributed computer environment. Some approaches address the problem of uncertainty, but many of them concentrate more on representation and less on evaluation. The emphasis in this paper is on evaluation and even though the representation used is that of probability theory, other well-established formalism can be used. The approach allows the decision maker to be as deliberately imprecise as he feels is natural and provides him with the means for expressing varying degrees of imprecision in the input sentences. The framework we present is intended to be tolerant and to provide means for evaluating decision situations using several decision rules beside the conventional maximisation of the expected utility.

MSC:

91B06 Decision theory
90B50 Management decision making, including multiple objectives
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[1] Allais, M., Fondements d’une théorie positive des choix comportant un risque et critique des postulate et axioms de I’Ecole Americane, (Expected Utility Hypothesis and the Allais Paradox (1953), D. Reidel Publishing Company), Translated into · Zbl 0053.28205
[2] Boman, M.; Ekenberg, L., Eliminating paraconsistencies in 4-valued cooperative deductive multidatabase systems with classical negation, (Proc. Cooperating Knowledge Based Systems (1994), Keele University Press), 161-176
[3] Boman, M.; Ekenberg, L., Decision making agents with relatively unbounded rationality, (Proc. DIMAS 1995 (1995)), invited paper
[4] Chen, S.-J.; Hwang, C.-L., Fuzzy multiple attribute decision making, (lecture notes in: Economics and Mathematical Systems (1992), Springer-Verlag), 375
[5] Choquet, G., Theory of capacities, Ann. Inst. Fourier, 5, 131-295 (1953/54) · Zbl 0064.35101
[6] Dempster, A. P., Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics, 38, 325-339 (1967) · Zbl 0168.17501
[7] Ekenberg, L.; Danielson, M., A support system for real-life decisions in numerically imprecise domains, (Proc. Int. Conference on Operations Research (1994), SpringerVerlag), 500-505 · Zbl 0827.90082
[8] Ekenberg, L.; Danielson, M., Handling imprecise information in risk management, (Proc. 11th IFIP SEC Conference (1995), Chapman and Hall: Chapman and Hall 357-368)
[9] Ekenberg, L.; Boman, M.; Danielson, M., A tool for coordinating autonomous agents with conflicting goals, (Proc. ICMAS 1995 (1995), AAAI/MIT Press), 89-93
[10] Ekenberg, L.; Oberoi, S.; Orci, I., A cost model for managing information security hazards, Computers and Security, 14, 707-717 (1995)
[11] Ekenberg, L.; Danielson, M.; Boman, M., From local assessments to global rationality, International Journal of Cooperative Information Systems, 5/2-3, 315-331 (1996)
[12] Ekenberg, L.; Danielson, M.; Boman, M., Imposing security constraints on agent-based decision support, Decision Support Systems Int. Journal (1996), to appear
[13] Ekenberg, L.; Danielson, M.; Boman, M., A tool for handling uncertain information in multi-agent systems, (Proc. MAAMAW 1994, lecture notes in Al 1069 (1996), SpringerVerlag), 54-62
[14] Fishbum, P., Subjective expected utility: A review of normative theories, Theory and Decision, 13, 139-199 (1981) · Zbl 0452.90004
[15] Gärdenfors, P.; Sahlin, N-E., Unreliable probabilities, risk taking and decision making, Synthese, 53, 361-386 (1982) · Zbl 0516.62011
[16] Good, I. J., Subjective probability as the measure of a non-measurable set, (Suppes, Nagel Tarski, Logic, Methodology and the Philosophy of Science (1962), Stanford University Press), 319-329 · Zbl 0192.02104
[17] Howard, R. A.; Matheson, J. E., Influence diagrams, (Howard, R. A.; Matheson, J. E., Principles and Applications of Decision Analysis, Vol. 11 (1984), Strategic Decisions Group: Strategic Decisions Group enlo Park, CA, USA)
[18] Huber, P. J.; Strassen, V., Minimax tests and the Neyman-Pearsons lemma for capacities, Annals of Statistics, l, 251-263 (1973) · Zbl 0259.62008
[19] Huber, P. J., The case of Choquet capacities in statistics, Bulletin of the International Statistical Institute, 45/4, 181-188 (1973)
[20] Hurwicz, L., Optimality criteria for decision making under ignorance, Cowles Commission Discussion Paper, 370 (1951)
[21] Jeffrey, R., The Logic of Decision, ((1983), University of Chicago Press), (1st Ed., 1965)
[22] Lai, Y-J.; Hwang, C-L., Fuzzy multiple objective decision making, (lecture notes in: Economics and Mathematical Systems (1994), Springer-Verlag), 404
[23] Lehmann, E. L., Testing Statistical Hypothesis (1959), John Wiley and Sons · Zbl 0089.14102
[24] Levi, I., On indeterminate probabilities, The Journal of Philosophy, 71, 391-418 (1974)
[25] Malmnäs, P-E., Towards a mechanization of real life decisions, (Prawitz; Westerståhl, Logic and Philosophy of Science in Uppsala (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 231-243
[26] Malmdäs, P-E., Axiomatic justification of the utility principle, Synthese, 99, 233-249 (1994)
[27] Nilsson, N., Probabilistic logic, Artificial Intelligence, 28, 71-87 (1986) · Zbl 0589.03007
[28] Saaty, T. L., The Analytical Hierarchy Process (1980), McGrawHill · Zbl 1176.90315
[29] Sage, A. P.; White, C. C., ARIADNE: A knowledgebased interactive system for planning and decision support, IEEE Transactions SMC, 14, 1 (1984)
[30] Salo, A. A.; Hämäläinen, R. P., Preference programming through approximate ratio comparisons, European Journal of Operational Research, 82/3, 458-475 (1995) · Zbl 0909.90006
[31] Savage, L., The Theory of statistical decision, Journal of the American Statistical Association, 46, 55-67 (1951) · Zbl 0042.14302
[32] Schoemaker, P., The expected utility model: Its variants, purposes, evidence and limitations, Journal of Economic Literature, 20, 529-563 (1982)
[33] Shachter, R. D., Evaluating Inference Diagrams, Operations Research, Vol. 34, No. 6 (1986), (reprinted in: G. Shafer and J. Pearl, Readings in Uncertain Reasoning
[34] Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press · Zbl 0359.62002
[35] Smith, C. A.B., Consistency in statistical inference and decision, Journal of the Royal Statistic Society Ser. B, 23, 1-25 (1961) · Zbl 0124.09603
[36] Wald, A., Statistical Decision Functions (1950), John Wiley and Sons · Zbl 0040.36402
[37] Weichselberger, K.; Pöhlman, S., A methodology for uncertainty in knowledge-based systems, (lecture notes in: Artificial Intelligence (1990), Springer-Verlag)
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