Abstract
The 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 a function 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. Apart from a better expressivity, the benefits of a logical representation of preferences are to put them in a suitable format for reasoning purposes, or for modifying them.
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R. Bellman and L.A. Zadeh, “Decision-making in a fuzzy environment,” Management Sciences, vol. 17, pp. 141-164, 1970.
S. Benferhat, D. Dubois, and H. Prade, “Representing default rules in possibilistic logic,” in Proc. KR'92, 1992, pp. 673-684.
S. Benferhat, D. Dubois, and H. Prade, “Reasoning in inconsistent stratified knowledge bases,” in Proc. of the 26 Inter. Symp. on Multiple-Valued Logic (ISMVL'96), Santiago de Compostela, Spain, May 29-31, 1996, pp. 184-189.
S. Benferhat, D. Dubois, and H. Prade, “Nonmonotonic reasoning, conditional objects and possibility theory,” Artificial Intelligence, vol. 92, pp. 259-276, 1997.
S. Benferhat, D. Dubois, and H. Prade, “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, edited by B. Bouchon-Meunier, Physica. Verlag, pp. 141-161, 1997.
S. Benferhat, D. Dubois, and H. Prade, “Practical handling of exception-tainted rules and independence information in possibilistic logic,” Applied Intelligence, vol. 9, pp. 101-127, 1998.
S. Benferhat, D. Dubois, and H. Prade, “Towards a possibilistic logic handling of preferences,” in Proc. 16th Int. Joint Conf. on Artificial Intelligence (IJCAI-99), Stockholm, Sweden, July 31-August 6, 1999, pp. 1370-1375.
S. Benferhat and L. Garcia, “Dealing with locally-prioritized inconsistent knowledge bases and its application to default reasoning,” in Applications of Uncertainty Formalisms, edited by T. Hunter and S. Parsons, LNAI1455, Springer, 1997.
C. Boutilier, “Toward a logic for qualitative decision theory,” in Proc. of the 4th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR-94), Bonn, edited by J. Doyle, E. Sandewall, P. Torasso, Morgan Kaufmann, pp. 75-86, 1994.
C. Boutilier, R.I. Brafman, H.H. Hoos, and D. Poole, “Reasoning with conditional ceteris paribus preference statements,” in Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence (UAI99), edited by K.B. Laskey and H. Prade, Morgan Kaufmann, pp. 71-80, 1999.
J.Doyle and M.P.Wellman, “Preferential semantics for goals,” in Proc. of the 9th National Conf. on Artificial Intelligence (AAAI-90), Anaheim, 1991, pp. 698-703.
D. Dubois, H. Fargier, and H. Prade. “Refinements of the maximin approach to decision-making in a fuzzy environment,” Fuzzy Sets and Systems, vol. 81, 1996, pp. 103-122.
D. Dubois, L. Farinas, A. Herzig, and H. Prade, “Qualitative relevance and independence: A roadmap,” in Proc. IJCAI-97, 1997, pp. 62-67.
D. Dubois, J. Lang, and H. Prade, “Theorem proving under uncertainty–A possibility theory-based approah,” in Proc. of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), 1987, pp. 984-986.
D. Dubois, J. Lang, and H. Prade, “Automated reasoning using possibilistic logic: Semantics, belief revision and variable certainty weights,” IEEE Trans. on Data and Knowledge Engineering, vol. 6, no. 1, pp. 64-71, 1994.
D. Dubois, D. Le Berre, H. Prade, and R. Sabbadin, “Logical representation and computation of optimal decisions in a qualitative setting,” in Proc. AAAI-98, 1998, pp. 588-593.
D. Dubois and H. Prade, “Necessity measures and the resolution principle,” IEEE Trans. Systems, Man and Cybernetics, vol. 17, pp. 474-478, 1987.
D. Dubois and H. Prade, “A synthetic view of belief revision with uncertain inputs in the framework of possibility theory,” Int. J. Approx. Reasoning, vol. 17, pp. 295-324, 1997.
D. Dubois and H. Prade, “Possibility theory: Qaulitative and quantitative aspects,” in Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Academic Press, vol. 1, pp. 169-226, 1998.
D. Dubois and H. Prade “Possibilistic logic in decision,” in Fuzzy Logic and Soft Computing, edited by Guoqing Chen, Mingsheng Ying, and Kai-Yuan Cai, Kluwer Academic Press, 1999.
R. Felix, “Towards a goal-oriented application of aggregation operators in fuzzy decision-making,” in Proc. of the Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU-92), Mallorca, July 6-10, 1992, pp. 585-588.
M. Grabisch, “The application of fuzzy integrals in multicriteria decision making,” Europ. J. of Operational Research, vol. 89, pp. 445-456, 1996.
M. Grabisch, H.T. Nguyen, and E.A. Walker, Fundamentals of Uncertainty Calculi, with Applications to Fuzzy Inference, Kluwer Academic, 1995.
S. Greco, B. Matarazzo, and R. Slowinski “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), edited by R. Felix, Dortmund, Germany, June 16-17, pp. 1-28, 1998.
M. Lacroix and P. Lavency “Preferences: Putting more knowledge into queries,” in Proc. of the 13rd Inter. Conf. on Very Large Data Bases, Brighton, UK, 1987, pp. 215-225.
J. Lang, “Possibilistic logic as a logical framework for minmax discrete optimisation problems and prioritized constraints,” in Fundamentals of Artificial Intelligence Research (FAIR'91), edited by P. Jorrand and J. Kelemen, L.N.C.S. no. 535, Springer Verlag, pp. 112-126, 1991.
J. Lang, “Logique possibiliste: Aspects formels, déduction automatique, et applications,” Ph.D. Thesis, Universite P. Sabatier, Toulouse, France, January 1991.
J. Lang, “Conditional desires and utilities–an alternative logical framework for qualitative decision theory,” in Proc. 12th European Conf. on Artif. Intellig.(ECAI-96), Budapest, Wiley, U.K., 1996, pp. 318-322.
J. Moura Pires and H. Prade, “Logical analysis of fuzzy constraint satisfaction problems,” in Proc. of the 1998 IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE'98), Anchorage, Alaska, May 4-9, 1998, pp. 857-862.
J. Moura-Pires, D. Dubois, and H. Prade, “Fuzzy constraint problems with general aggregation operations under possibilistic logic form,” in Proc. 6th Europ. Cong. on Intellig. Techniques & Soft Comput., Aachen, Germany, September 7-10, 1998, pp. 535-539.
J. Ryan and M.-A. Williams, “Modelling changes in preference: an implementation, ISRR-027-1997, Dept. of Management, University” of Newcastle, NSW, Australia, 1997.
T. Schiex. “Possibilistic constraint satisfaction problems or How to handle soft constraints?,” in Proc. of the 8th Conf. on Uncertainty in Artificial Intelligence (UAI92), edited by D. Dubois, M.P. Wellman, B. D'Ambrosio, and P. Smets, Morgan Kaufmann, pp. 268-275, 1992.
W. Spohn, “Ordinal conditional functions: A dynamic theory of epistemic states,” in Causation in Decicion, Belief Change and Statistics, edited by W.L. Harper and B. Skyrms, Reidel, Dordrecht, vol. 2, pp. 105-134, 1988.
S.-W. Tan and J. Pearl, “Qualitative decision theory,” in Proc. of the 12th National Conf. on Artificial Intelligence (AAAI-94), Seattle, WA, July 31-Aug. 4, 1994, pp. 928-933.
L. Van der Torre and E.Weydert, “Parameters for utilitarian desires in qualitative decision theory,” Applied Intelligence, 2000, this issue.
M.-A. Williams, “Transmutations of knowledges systems,” in Proc. KR-94, 1994, pp. 619-629.
R.R. Yager, “On the specificity of a possibility distribution,” Fuzzy Sets and Systems, vol. 50, pp. 279-292, 1992.
L.A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, pp. 3-28, 1978.
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Benferhat, S., Dubois, D. & Prade, H. Towards a Possibilistic Logic Handling of Preferences. Applied Intelligence 14, 303–317 (2001). https://doi.org/10.1023/A:1011298804831
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DOI: https://doi.org/10.1023/A:1011298804831