Abstract
This paper is a survey of qualitative decision theory focusing on available decision rules under uncertainty, and their properties. It is pointed out that two main approaches exist according to whether degrees of uncertainty and degrees of utility are commensurate (that is, belong to a unique scale) or not. Savage-like axiom systems for both approaches are surveyed. In such a framework, acts are functions from states to results, and decision rules are derived from first principles, bearing on a preference relation on acts. It is shown that the emerging uncertainty theory in qualitative settings is possibility theory rather than probability theory. However these approaches lead to criteria that are either little decisive due to incomparability, or too adventurous because focusing on the most plausible states, or yet lacking discrimination because or the coarseness of the value scale. Some suggestions to overcome these defects are pointed out.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arrow K. (1951). Social Choice and Individual Values. New York, N.Y.: Wiley.
Arrow, K. Hurwicz L. (1972). An optimality criterion for decision-making under ignorance. In: C.F. Carter, J.L. Ford, eds., Uncertainty and Expectations in Economics. Oxford, UK: Basil Blackwell & Mott Ltd.
Bacchus F. and Grove A. (1996). Utility independence in a qualitative decision theory. In: Proc. Of the 5rd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’96), Cambridge, Mass., 542–552.
Benferhat S., Dubois D., Prade H. (1999) Possibilistic and standard probabilistic semantics of conditional knowledge bases. J. Logic and Computation, 9, 873–895.
Boutilier C. (1994). Towards a logic for qualitative decision theory. In: Proc. of the 4rd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’94), Bonn, Germany, May. 2427, 75–86.
Bouyssou D., Marchant T., Pirlot M., Perny P., Tsoukias A. and Vincke P. (2000). Evaluation Models: a Critical Perspective. Kluwer Acad. Pub. Boston.
Brafman R.I., Tennenholtz M. (1997). Modeling agents as qualitative decision makers. Artificial Intelligence, 94, 217–268.
Brafman R.I., Tennenholtz M. (2000). On the Axiomatization of Qualitative Decision Criteria, J. ACM, 47, 452–482
Buckley J. J. (1988) Possibility and necessity in optimization, Fuzzy Sets and Systems, 25, 1–13.
Cayrol M., Farreny H. (1982). Fuzzy pattern matching. Kybernetes, 11, 103–116.
Cohen M. and Jaffray J.-Y. (1980) Rational behavior under complete ignorance. Econometrica, 48, 1280–1299.
Doyle J., Thomason R. (1999). Background to qualitative decision theory. The AI Magazine, 20 (2), 1999, 55–68
Doyle J., Wellman M.P. (1991). Impediments to universal preference-based default theories. Artificial Intelligence, 49, 97–128.
Dubois D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence (Bratislava), 5 (5), 403–416.
Dubois D. (1987) Linear programming with fuzzy data, In: The Analysis of Fuzzy Information — Vol. 3: Applications in Engineering and Science ( J.C. Bezdek, ed.), CRC Press, Boca Raton, Fl., 241–263
Dubois D., Fargier H., and Prade H. Fuzzy constraints in job-shop scheduling. J. of Intelligent Manufacturing, 64: 215–234, 1995.
Dubois D., Fargier H., and Prade H. (1996). Refinements of the maximin approach to decision-making in fuzzy environment. Fuzzy Sets and Systems, 81, 103–122.
Dubois D., Fargier H., and Prade H. (1997). Decision making under ordinal preferences and uncertainty. In: Proc. of the 13th Conf. on Uncertainty in Artificial Intelligence ( D. Geiger, P.P. Shenoy, eds.), Providence, RI, Morgan & Kaufmann, San Francisco, CA, 157–164.
Dubois D., Fargier H., and Perny P. (2001). Towards a qualitative multicriteria decision theory. In: Proceedings of Eurofuse Workshop on Preference Modelling and Applications, Granada, Spain, 121–129, 25–27 avril 2001. To appear in Int. J. Intelligent Systems, 2003.
Dubois D., Fargier H., Perny P. and Prade H. (2002a). Qualitative Decision Theory: from Savage’s Axioms to Non-Monotonic Reasoning. Journal of the ACM, 49, 455–495.
Dubois D., Fargier H., and Perny P. (2002b). On the limitations of ordinal approaches to decision-making. Proc. of the 8th International Conference, Principles of Knowledge Representation and Reasoning (KR2002), Toulouse, France. Morgan Kaufmann Publishers, San Francisco, California, 133–144.
Dubois D., Fargier H., and Perny P. (2003). Qualitative models for decision under uncertainty: an axiomatic approach. Artificial Intell., to appear.
Dubois D., Fortemps P. (1999). Computing improved optimal solutions to max-min flexible constraint satisfaction problems. European Journal of Operational Research, 118, p. 95–126.
Dubois D., Grabisch M., Modave F., Prade H. (2000) Relating decision under uncertainty and multicriteria decision making models. Int. J. Intelligent Systems, 151, 967–979.
Dubois D., Marichal J.L., Prade H., Roubens M., Sabbadin R. (2001) The use of the discrete Sugeno integral in decision-making: a survey. Int. J. Uncertainty, Fuzziness and Knowledge-based Systems, 9, 539–561.
Dubois D., Prade H. (1988) Possibility Theory — An Approach to the Computerized Processing of Uncertainty. Plenum Press, New York
Dubois D., Prade H. (1995a) Numerical representation of acceptance. In: Proc. of the 11th Conf. on Uncertainty in Articicial Intelligence, Montréal, August, 149–156.
Dubois D., Prade H.(1995ó) Possibility theory as a basis for qualitative decision theory. In: Proc. of the Inter. Joint Conf. on Artificial Intelligence (IJCAI’95), Montréal, August, 1924–1930.
Dubois D., Prade H. (1998). Possibility theory: qualitative and quantitative aspects. P. Smets, (Eds), In: Handbook on Defeasible Reasoning and Uncertainty Management Systems — Volume 1: Quantified Representation of Uncertainty and Imprecision. Kluwer Academic Publ., Dordrecht, The Netherlands, 169–226
Dubois D., Prade H., and Sabbadin R. (1998). Qualitative decision theory with Sugeno integrals.Proceedings of 14th Conference on Information Processing and Management of Uncertainty in Artificial Intelligence (UAI’98), Madison, WI, USA. Morgan Kaufmann, San Francisco, CA, p. 121–128.
Dubois D., Prade H., and Sabbadin R. (2001). Decision-theoretic foundations of possibility theory. European Journal of Operational Research, 128, 459–478.
Dubois D., Prade H., Testemale C. (1988). Weighted fuzzy pattern matching. Fuzzy Sets and Systems, 28, 313–331.
Fargier H., Lang J. and Schiex T. (1993) Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems, In: Proc. of the 1st Europ. Conf. on Fuzzy Information Technologies (EUFIT’93), Aachen, Germany, 1128–1134.
Fargier H., Perny P. (1999). Qualitative models for decision under uncertainty without the commensurability assumption. In: Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence ( K. Laskey, H. Prade, eds.), Providence, RI, Morgan & Kaufmann, San Francisco, CA, 157–164.
Fargier H., Lang J., Sabbadin R. (1998). Towards qualitative approaches to multi-stage decision making. International Journal of Approximate Reasoning, 19, 441–471.
Fargier H., Sabbadin R., (2000) Can qualitative utility criteria obey the surething principle? Proceedings IPMU2000, Madrid, 821–826.
Fargier H. Sabbadin R. (2003) Qualitative decision under uncertainty: back to expected utility, Proc. IJCAI’03, Acapulco, Mexico.
Fishburn P. (1975). Axioms for lexicographic preferences. Review of Economical Studies, 42, 415–419
Fishburn P. (1986). The axioms of subjective probabilities. Statistical Science 1, 335–358.
Friedman N., Halpern J. (1996). Plausibility measures and default reasoning. Proc of the 13th National Conf on Artificial Intelligence (AAAI’96), Portland, 1297–1304.
Giang P., Shenoy P. (2000). A qualitative utility theory for Spohn’s theory of epistemic beliefs. In: Proc. of the 16th Conf. on Uncertainty in Artificial Intelligence, 220–229.
Giang P., Shenoy P. (2001). A comparison of axiomatic approaches to qualitative decision-making using possibility theory. Proc. 17 th Int. Conf. on Uncertainty in Artificial Intelligence, 162–170.
Grabisch M., Murofushi T., Sugeno M., Eds. (1999) Fuzzy Measures and Integrals Physica-Verlag, Heidelberg, Germany.
Grabisch M., De Baets B., and Fodor J. (2002) On symmetric pseudo-additions and pseudo-multiplications: is it possible to build rings on [-1, +1]? In: Proc. 9th Int Conf. on Information Processing and Management of Uncertainty in Knowledge based Systems (IPMU2002), Annecy, France, pp 1349–1355.
Grant S., Kajii A., Polak B. (2000) Decomposable Choice under Uncertainty, J. Economic Theory. Vol. 92, No. 2, pp. 169–197.
Jaffray J.-Y. (1989) Linear utility theory for belief functions. Operations Research Letters, 8, 107–112.
Inuiguichi M., Ichihashi H., and Tanaka, H. (1989). Possibilistic linear programming with measurable multiattribute value functions. ORSA J. on Computing, 1, 146–158.
Kraus K., Lehmann D, Magidor M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.
Lang J. (1996). Conditional desires and utilities: an alternative logical approach to qualitative decision theory. Proc. of the 12th European Conf. on Artificial Intelligence (ECAI’96), Budapest, 318–322.
Lehmann D. (1996). Generalized qualitative probability: Savage revisited. Proc. of the 12th Conf. on Uncertainty in Artificial Intelligence, Portland, August, Morgan & Kaufman, San Mateo, CA, 381–388.
Lehmann D. (2001). Expected Qualitative Utility Maximization, J. Games and Economic Behavior. 35, 54–79
Lewis D. (1973). Counterfactuals. Basil Blackwell, London.
Moulin H. (1988). Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge, MA.
Roubens M., Vincke P. (1985) Preference Modelling. Lecture Notes in Economics and Mathematical Systems, Vol. 250, Springer Verlag, Berlin.
Sabbadin R. (2000), Empirical comparison of probabilistic and possibilistic Markov decision processes algorithms. Proc. 14 th Europ. Conf. on Artificial Intelligence (ECAI’00), Berlin, Germany, 586–590.
Savage L.J. (1972). The Foundations of Statistics. Dover, New York.
Schmeidler D. (1989) Subjective probability and expected utility without additivity, Econometrica, 57, 571–587.
Sen A.K. (1986). Social choice theory. In K. Arrow, M.D. Intrilligator, Eds., Handbook of Mathematical Economics, Chap. 22, Elsevier, Amsterdam, 1173–1181.
Shackle G.L.S. (1961) Decision Order and Time In Human Affairs Cambridge University Press, Cambridge, U.K.(2nd edition, 1969).
Snow P. (1999) Diverse confidence levels in a probabilistic semantics for conditional logics. Artificial Intelligence 113, 269–279.
Tan S.W., Pearl J. (1994). Qualitative decision theory. Proc. 11th National Conf. on Artificial Intelligence (AAAI-94), Seattle, WA, pp. 70–75.
Thomason R. (2000), Desires and defaults: a framework for planning with inferred goals. In: Proc. of the Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’00), Breckenridge, Col.., Morgan & Kaufmann, San Francisco, 702–713.
VonNeumannJ. and Morgenstern O. (1944): Theory of Games and Economic Behaviour (Princeton Univ. Press, Princeton, NJ).
Vincke P. Multicriteria Decision-Aid, J. Wiley & Sons, New York, 1992
Wald A. (1950), Statistical Decision Functions. J. Wiley & Sons, New York.
Whalen T. (1984). Decision making under uncertainty with various assumptions about available information. IEEE Trans. on Systems, Man and Cybernetics, 14: 888–900.
Yager.R.R. (1979). Possibilistic decision making. IEEE Trans. on Systems, Man and Cybernetics, 9: 388–392.
L.A. Zadeh L.A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Wien
About this chapter
Cite this chapter
Dubois, D., Fargier, H. (2003). Qualitative Decision Rules Under Uncertainty. In: Della Riccia, G., Dubois, D., Kruse, R., Lenz, HJ. (eds) Planning Based on Decision Theory. International Centre for Mechanical Sciences, vol 472. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2530-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2530-4_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-40756-1
Online ISBN: 978-3-7091-2530-4
eBook Packages: Springer Book Archive