Skip to main content
Springer Nature Link
Log in

Qualitative Decision Rules under Uncertainty

  • Conference paper
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2711))

  • 904 Accesses

Abstract

This paper is a survey of qualitative decision theory focused on the 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 axiomatics for both approaches are surveyed. In such a framework, acts are functions from states to results, and decision rules are used to characterize 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 incomparabilities, or too adventurous because focusing on the most plausible states, or yet lacking discrimination because or the coarseness of the value scale. Some new results overcoming these defects are reviewed. Interestingly, they lead to genuine qualitative counterparts to expected utility.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bacchus, F., Grove, A.: Utility independence in a qualitative decision theory. In: Proc. of the 5th Inter. Conf. on Princ. Of Know. Repres. and Reas. (KR 1996), Cambridge, Mass, pp. 542–552 (1996)

    Google Scholar 

  2. Benferhat, S., Dubois, D., Prade, H.: Possibilistic and standard probabilistic semantics of conditional knowledge. J. Logic and Computation 9, 873–895 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Boutilier, C.: Towards a logic for qualitative decision theory. In: Proc. of the 4rd Inter. Conf. on Princ. of Knowl. Repres. and Reason. (KR 1994), Bonn, Germany, pp. 75–86 (1994)

    Google Scholar 

  4. Brafman, R.I., Tennenholtz, M.: Modeling agents as qualitative decision makers. Artificial Intelligence 94, 217–268 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Brafman, R.I., Tennenholtz, M.: On the Axiomatization of Qualitative Decision Criteria. J. ACM 47, 452–482 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cohen, M., Jaffray, J.: Rational behavior under complete ignorance. Econometrica 48, 1280–1299 (1980)

    Article  MathSciNet  Google Scholar 

  7. Doyle, J., Thomason, R.: Background to qualitative decision theory. The AI Magazine 20(2), 55–68 (Summer 1999)

    Google Scholar 

  8. Dubois, D.: Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and AI (Bratislava) 5(5), 403–416 (1986)

    MATH  Google Scholar 

  9. Dubois, D., Fargier, H., Prade, H.: Refinements of the maximin approach to decision-making in fuzzy environment. Fuzzy Sets and Systems 81, 103–122 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dubois, D., Fargier, H., Prade, H.: Decision making under ordinal preferences and uncertainty. In: Proc. of the 13th Conf. on Uncertainty in AI, Providence, RI, pp. 157–164. Morgan & Kaufmann, San Francisco (1997)

    Google Scholar 

  11. Dubois, D., Fargier, H., Perny, P.: Towards a qualitative multicriteria decision theory. Int. in J. Intelligent Systems (2001) (to appear)

    Google Scholar 

  12. Dubois, D., Fargier, H., Perny, P., Prade, H.: Qualitative Decision Theory: from Savage’s Axioms to Non-Monotonic Reasoning. Journal of the ACM 49, 455–495 (2002)

    Article  MathSciNet  Google Scholar 

  13. Dubois, D., Fargier, H., Perny, P.: On the limitations of ordinal approaches to decision-making. In: Proc.of the 8th Int. Conf., Principles of Knowledge Repres. and Reasoning (KR 2002), Toulouse, France, pp. 133–144. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  14. Dubois, D., Fargier, H., Perny, P.: Qualitative Decision Theory with preference relations and comparative uncertainty: an axiomatic aproach. Artificial Intelligence (2003) (to appear)

    Google Scholar 

  15. Dubois, D., Fargier, H., Sabbadin, R.: Additive refinements of qualitative decision criteria. 24th Int. Seminar on Fuzzy Set Theory, Linz (2003)

    Google Scholar 

  16. Dubois, D., Fortemps, P.: Computing improved optimal solutions to max-min flexible constraint satisfaction problems. Eur. J. of Oper. Res. 118, 95–126 (1999)

    Article  MATH  Google Scholar 

  17. Dubois, D., Godo, L., Prade, H., Zapico, A.: On the possibilistic decision model: from decision under uncertainty to case-based decision. Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 7, 631–670 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Dubois, D., Prade, H.: Possibility theory as a basis for qualitative decision theory. In: Proc. IJCAI 1995, Montréal, Canada, pp. 1924–1930 (1995)

    Google Scholar 

  19. Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Smets, P. (ed.) Handbook on Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer Academic Publ., Dordrecht (1998)

    Google Scholar 

  20. Dubois, D., Prade, H., Sabbadin, R.: Qualitative decision theory with Sugeno integrals. In: Proc. of 14th Conf. on Uncertainty in AI (UAI 1998), Madison, WI, USA, pp. 121–128. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  21. Dubois, D., Prade, H., Sabbadin, R.: Decision-theoretic foundations of possibility theory. European Journal of Operational Research 128, 459–478 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. Fargier, H., Perny, P.: Qualitative models for decision under uncertainty without the commensurability assumption. In: Proc. of the 15th Conf. on Uncertainty in AI, Providence, RI, pp. 157–164. Morgan & Kaufmann, San Francisco (1999)

    Google Scholar 

  23. Fargier, H., Lang, J., Sabbadin, R.: Towards qualitative approaches to multi-stage decision making. International Journal of Approximate Reasoning 19, 441–471 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  24. Fargier, H., Sabbadin, R.: Can qualitative utility criteria obey the surething principle?. In: Proceedings IPMU2000, Madrid, pp. 821–826 (2000)

    Google Scholar 

  25. Fargier, H., Sabbadin, R.: Qualitative decion under uncertainty: back to expected utility. In: Proc. IJCAI 2003, Acapulco, Mexico (2003)

    Google Scholar 

  26. Fishburn, P.: Axioms for lexicographic preferences. Rev. Econ. Stud. 42, 415–419 (1975)

    Article  MATH  Google Scholar 

  27. Friedman, N., Halpern, J.: Plausibility measures and default reasoning. In: Proc of the 13th National Conf. on AI (AAAI 1996), Portland, pp. 1297–1304 (1996)

    Google Scholar 

  28. Giang, P., Shenoy, P.: A comparison of axiomatic approaches to qualitative decision- making using possibility theory. In: Proc. 17th Int. Conf. on Uncertainty in AI, pp. 162–170. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  29. Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integrals. Physica- Verlag, Heidelberg (2000)

    MATH  Google Scholar 

  30. Kraus, K., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  31. Lang, J.: Conditional desires and utilities: an alternative logical approach to qualitative decision theory. In: Proc. 12th Eur. Conf. on AI (ECAI 1996), Budapest, pp. 318–322 (1996)

    Google Scholar 

  32. Lehmann, D.: Generalized qualitative probability: Savage revisited. In: Proc. 12th Conf. on Uncertainty in AI, Portland, pp. 381–388. Morgan & Kaufman, San Mateo (1996)

    Google Scholar 

  33. Lehmann, D.: Expected Qualitative Utility Maximization. J. Games and Economic Behavior 35, 54–79 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  34. Lewis, D.: Counterfactuals. Basil Blackwell, London (1973)

    Google Scholar 

  35. Sabbadin, R.: Empirical comparison of probabilistic and possibilistic Markov decision processes algorithms. In: Proc. 14th Eur. Conf. on AI (ECAI 2000), Berlin, Germany, pp. 586–590 (2000)

    Google Scholar 

  36. Savage, L.J.: The Foundations of Statistics. Dover, New York (1972)

    MATH  Google Scholar 

  37. Snow, P.: Diverse confidence levels in a probabilistic semantics for conditional logics. Artificial Intelligence 113, 269–279 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  38. Tan, S.W., Pearl, J.: Qualitative decision theory. In: Proc. 11th National Conf. on AI (AAAI 1994), Seattle, WA, pp. 70–75 (1994)

    Google Scholar 

  39. Thomason, R.: Desires and defaults: a framework for planning with inferred goals. In: Proc. of the Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR 2000), Breckenridge, Col., pp. 702–713. Morgan & Kaufmann, San Francisco (2000)

    Google Scholar 

  40. Whalen, T.: Decision making under uncertainty with various assumptions about available information. IEEE Trans. on Systems, Man and Cybernetics 14, 888–900 (1984)

    MathSciNet  Google Scholar 

  41. Yager, R.R.: Possibilistic decision making. IEEE Trans. on Systems, Man and Cybernetics 9, 388–392 (1979)

    Article  MathSciNet  Google Scholar 

  42. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRIT, Université Paul Sabatier, 31062, Toulouse Cedex 4, France

    Didier Dubois & Hélène Fargier

  2. INRA-BIA, Chemin de Borde Rouge, B.P37, 31326, Castanet-Tolosan cedex

    Régis Sabbadin

Authors
  1. Didier Dubois
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hélène Fargier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Régis Sabbadin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Aalborg University, Fredrik Bajersvej 7E, 9220, Aalborg, Denmark

    Thomas Dyhre Nielsen

  2. Department of Computer Science, Hong Kong University of Science and Technology, ClearWater Bay Road, Kowloon, Hong Kong, China,

    Nevin Lianwen Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dubois, D., Fargier, H., Sabbadin, R. (2003). Qualitative Decision Rules under Uncertainty. In: Nielsen, T.D., Zhang, N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science(), vol 2711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45062-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45062-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40494-1

  • Online ISBN: 978-3-540-45062-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics