Abstract
A classical way of encoding preferences in decision theory is by means of utility or value functions. However agents are not always able to deliver such functions directly. In this paper, we relate three different ways of specifying preferences, namely by means of a set of particular types of constraints on the utility function, by means of an ordered set of prioritized goals expressed by logical propositions, and by means of an ordered set of subsets of possible choices reaching the same level of satisfaction. These different expression modes can be handled in a weighted logical setting, here the one of possibilistic logic. The aggregation of preferences pertaining to different criteria can then be handled by fusing sets of prioritized goals. A logical representation is not only expressive, but also enable preferences to be reasoned about, and revised in a more transparent way.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bellman R., Zadeh L.A. (1970) Decision-making in a fuzzy environment. Management Sciences, 17, 141–164.
Benferhat S., Dubois D., Prade H. (1996) Reasoning in inconsistent stratified knowledge bases. Proc. of the 26 Inter. Symp. on Multiple-Valued Logic (ISMVL′96), Santiago de Compostela, Spain, 29–31 May, 184–189.
Benferhat S., Dubois D., Prade H. (1997a) Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92, 259–276.
Benferhat S., Dubois D., Prade H. (1997b) From semantic to syntactic approaches to information combination in possibilistic logic. In: Aggregation and Fusion of Imperfect Information, Studies in Fuzziness and Soft Computing Series, (B. Bouchon-Meunier, ed.), Physica. Verlag, 141–161.
Benferhat S., Dubois D., Prade H. (1998) Practical handling of exception-tainted rules and independence information in possibilistic logic. Applied Intelligence, 9, 101–127.
Benferhat S., Dubois D., Prade H. (1999) Towards a possibilistic logic handling of preferences. Proc. 16th Int. Joint Conf. on Artificial Intelligence (IJCAI-99), Stockholm, Sweden, 31 July–6 august, 1999, 1370–1375.
Benferhat S., Garcia, L. (1998) Dealing with locally-prioritized inconsistent knowledge bases and its application to default reasoning. In Applications of Uncertainty Formalisms (T. Hunter, and S. Parsons eds.), LNAI 1455, Springer, Berlin, pages 323–353.
Boutilier C.(1994) Toward a logic for qualitative decision theory Proc. of the 4th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR-94), Bonn, (J.Doyle, E.Sandewall, P.Torasso, eds.), Morgan Kaufmann, 75–86.
Boutilier C, Brafman R. I., Hoos H.H., Poole D. (1999) Reasoning with conditional ceteris paribus preference statements. Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence (UAI99), (K.B. Laskey, H. Prade, eds.), Morgan Kaufmann, 71–80.
Doyle J., Wellman M.P. (1991) Preferential semantics for goals. In Proc. of the 9th National Conf. on Artificial Intelligence (AAAI-90), Anaheim, 698–703.
Dubois D., Fargier H., Prade H. (1996) Refinements of the maximin approach to decisionmaking in a fuzzy environment. Fuzzy Sets and Systems, 81, 103–122
Dubois D., Farinas L., Herzig A., Prade H., (1997) Qualitative relevance and independence: a roadmap. In Proceedings of the fiftheen International Joint Conference on Artificial Intelligence (IJCAI-97), 62–67.
Dubois D., Lang J., Prade H. (1994) Automated reasoning using possibilistic logic: semantics, belief revision and variable certainty weights. IEEE Trans, on Data and Knowledge Engineering, 6(1), 64–71.
Dubois D., Le Berre D., Prade H., Sabbadin R. (1998) Logical representation and computation of optimal decisions in a qualitative setting. Proc. AAAI-98, 588–593.
Dubois D., Prade H. (1987) Necessity measures and the resolution principle, IEEE Trans. Systems, Man and Cybernetics, Vol. 17, pp. 474–478.
Dubois D., Prade H. (1998) Possibility theory: qualitative and quantitative aspects. In Handbook of defeasible reasoning and uncertainty management systems. Vol. 1, pp. 169–226, Kluwer Academic Press.
Felix R. (1992) Towards a goal-oriented application of aggregation operators in fuzzy decision-making. Proc. of the Int. Conf. on Information Processing and Management of
Uncertainty in Knowledge Based Systems (IPMU-92), Mallorca, July 6–10, 585–588.
Grabisch M. (1996) The application of fuzzy integrals in multicriteria decision making. Europ. J. of Operational Research, 89, 445–456.
Grabisch M, H. T. Nguyen, and E. A. Walker (1995) Fundamentals of uncertainty calculi, with applications to fuzzy inference. Kluwer Academic.
Greco S., Matarazzo B., Slowinski R. (1998) Rough set theory approach to decision analysis. In Proc. 3rd Europ. Workshop on Fuzzy Decision Analysis and Neural Networks for Management, Planning and Optimization (EFDAN′98), (R. Felix, ed.), Dortmund, Germany, June 16–17, 1998, 1–28.
Keeney R. and Raiffa H. (1976). Decision with Multiple Objectives: Preferences and Value Trade-offs, Wiley, New York.
Lacroix M., Lavency P. (1987) Preferences: Putting more knowledge into queries. Proc. of the 13rd Inter. Conf. on Very Large Data Bases, Brighton, UK, 215–225.
Lang J. (1991a) Possibilistic logic as a logical framework for min-max discrete optimisation problems and prioritized constraints. In Fundamentals of Artificial Intelligence Research (FAIR′91), (P. Jorrand, J. Kelemen, eds.), L.N.C.S. n°535, Springer Verlag, 112–126.
Lang J. (1991b) Logique possibiliste: aspects formels, déduction automatique, et applications. PhD Thesis, Universite P. Sabatier, Toulouse, France, January 1991.
Lang J. (1996) Conditional desires and utilities — an alternative logical framework for qualitative decision theory. Proc. 12th European Conf. on Artif. Intellig. (ECAI-96), Budapest, Wiley, U.K., 318–322.
Minker J., ed. (2000) Logic-based Artifcial Intelligence. Kluwer Academics Publisher, Boston.
Moura Pires J., Prade H. (1998) Logical analysis of fuzzy constraint satisfaction problems. Proc. of the 1998 IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE′98), Anchorage, Alaska, May 4–9, 1998, 857–862.
Moura-Pires J., Dubois D., Prade H. (1998) Fuzzy constraint problems with general aggregation operations under possibilistic logic form. Proc. 6th Europ. Cong, on Intellig. Techniques & Soft Comput, Aachen, Germany, Sept. 7–10, 1998, pp. 535–539.
Roy B., Bouyssou D. (1993) Aide Multicritère à la Décision: Méthodes et Cas. Ed. Economica, Paris.
Ryan J., Williams, M.-A. (1997) Modelling changes in preference: an implementation. ISRR-027-1997, Dept. of Management, Univ. of Newcastle, NSW, Australia.
Schiex T. (1992) Possibilistic constraint satisfaction problems or “How to handle soft constraints?” In Proc. of the 8th Conf. on Uncertainty in Artificial Intelligence (UAI92), (D.Dubois, M.P.Wellman, B. D’Ambrosio, P. Smets, eds.), Morgan Kaufmann, 268–275.
Spohn W. (1988) Ordinal conditional functions: a dynamic theory of epistemic states. In: Causation in Decicion, Belief Change and Statistics, Vol. 2, (W.L.Harper and B.Skyrms, eds.), Reidel, Dordrecht, 105–134.
Tan S.-W., Pearl J. (1994) Qualitative decision theory. In: Proc. of the 12th National Conf. on Artificial Intelligence (AAAI-94), Seattle, Wa., July 31 – Aug. 4, 1994, 928–933.
Van der Torre L., Weydert E. (2001) Parameters for utilitarian desires in qualitative decision theory. Applied Intelligence, to appear.
Williams, M.-A. (1994) Transmutations of knowledges systems. Proc. KR-94, 619–629.
Yager R.R. (1992) On the specificity of a possibility distribution. Fuzzy Sets and Systems, 50, 279–292.
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
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Benferhat, S., Dubois, D., Prade, H. (2002). Towards a Possibilistic Logic Handling of Preferences. In: Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Słowiński, R., Vanderpooten, D., Vincke, P. (eds) Aiding Decisions with Multiple Criteria. International Series in Operations Research & Management Science, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0843-4_14
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0843-4_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5266-2
Online ISBN: 978-1-4615-0843-4
eBook Packages: Springer Book Archive