Qualitative possibility theory and its applications to constraint satisfaction and decision under uncertainty

This paper provides a brief survey and an introduction to the modeling capabilities of qualitatï e possibility theory in decision analysis for the representation and the aggregation of preferences, for the treatment of uncertainty and for the handling of situations similar to previously encountered ones. ‘‘Qualitative’’ here means that we restrict Ž ourselves to linearly ordered valuation sets only the ordering of the grades is meaning. ful for the assessment of preferences, uncertainty and similarity. Moreover, all the Ž . evaluations refer to the same valuation set commensurability assumption . Such a qualitative structure is poor but not very demanding from an elicitation point of view; however, it is sufficient for giving birth to a valuable set of modeling tools. Q 1999 John Wiley & Sons, Inc.

[1]  D. Dubois,et al.  Constraint satisfaction and decision under uncertainty based on qualitative possibility theory , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[2]  Hung T. Nguyen,et al.  Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference , 1994 .

[3]  Didier Dubois,et al.  Decision Evaluation Methods Under Uncertainty and Imprecision , 1988 .

[4]  Henri Prade,et al.  Fuzzy set modelling in case-based reasoning , 1998, Int. J. Intell. Syst..

[5]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[6]  J. Kacprzyk,et al.  Multiperson decision making models using fuzzy sets and possibility theory , 1990 .

[7]  Michel Grabisch,et al.  Relating Decision under Uncertainty and MCDM Models , 1997 .

[8]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[9]  Didier Dubois,et al.  Representing Default Rules in Possibilistic Logic , 1992, KR.

[10]  Leonid Kitainik,et al.  Fuzzy Decision Procedures with Binary Relations , 1993, Theory and Decision Library.

[11]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[12]  Didier Dubois,et al.  Possibility Theory as a Basis for Qualitative Decision Theory , 1995, IJCAI.

[13]  Didier Dubois,et al.  Reasoning in inconsistent stratified knowledge bases , 1996, Proceedings of 26th IEEE International Symposium on Multiple-Valued Logic (ISMVL'96).

[14]  Didier Dubois,et al.  Leximin optimality and fuzzy set-theoretic operations , 2001, Eur. J. Oper. Res..

[15]  Didier Dubois,et al.  Qualitative Decision Theory with Sugeno Integrals , 1998, UAI.

[16]  M. Lacroix,et al.  Preferences; Putting More Knowledge into Queries , 1987, VLDB.

[17]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[18]  Craig Boutilier,et al.  A Constraint-Based Approach to Preference Elicitation and Decision Making , 1997 .

[19]  Willi Hock,et al.  Lecture Notes in Economics and Mathematical Systems , 1981 .

[20]  Didier Dubois,et al.  Fuzzy rules in knowledge-based systems , 1992 .

[21]  Didier Dubois,et al.  Decision-Making under Ordinal Preferences and Comparative Uncertainty , 1997, UAI.

[22]  Didier Dubois,et al.  Logical Representation and Computation of Optimal Decisions in a Qualitative Setting , 1998, AAAI/IAAI.

[23]  L. Zadeh.  Calculus of fuzzy restrictions , 1996 .