Making Discrete Sugeno Integrals More Discriminant

International Journal of Approximate Reasoning

Volumn 50, Issue 6, 2009, Pages 880-898

  Dubois, Didier ^a   Fargier, Hélène ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Choquet integral; Lexicographic ordering; Qualitative decision theory; Sugeno integral

Indexed keywords

CHOQUET INTEGRAL; DECISION UNDER UNCERTAINTIES; ENCODINGS; LEXICOGRAPHIC METHODS; LEXICOGRAPHIC ORDERING; LEXIMIN; QUALITATIVE DECISION THEORY; QUALITATIVE EVALUATIONS; SUGENO INTEGRAL; WEIGHTED AVERAGES;

ENCODING (SYMBOLS); GAME THEORY; INTEGRAL EQUATIONS; NUMERICAL METHODS; REFINING;

DECISION THEORY;

EID: 67349157978     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2009.03.007     Document Type: Article

References (44)

1. Arrow K., and Hurwicz L. An optimality criterion for decision-making under ignorance. In: Carter C.F., and Ford J.L. (Eds). Uncertainty and Expectations in Economics (1972), Basil Blacwell and Mott Ltd
2. Arrow K.J. Social Choice and Individual Values (1951), Cowles Foundations and Wiley, New-York
3. Benferhat S., Dubois D., and Prade H. Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation 9 (1999) 873-895
4. C. Boutilier. Toward a logic for qualitative decision theory. In Proceedings of KR'94, pages 75-86, 1994.
5. D. Bouyssou, T. Marchant, and M. Pirlot, A conjoint measurement approach to the discrete Sugeno integral, in: S. Brams, W. Gehrlein, F. Roberts, (Eds.), The Mathematics of Preference, Choice and Order (Essays in Honor of Peter C. Fishburn), pages 1-25. 2008.
6. R. Brafman and M. Tennenholtz. On the foundations of qualitative decision theory. In Proceedings of AAAI'96, pages 1291-1296, 1996.
7. R. Brafman and M. Tennenholtz. On the axiomatization of qualitative decision theory. In Proceedings of AAAI'97, pages 76-81, 1997.
8. Brafman R., and Tennenholtz M. An axiomatic treatment of three qualitative decision criteria. Journal of the ACM 47 3 (2000) 452-482
9. Chateauneuf A. Decomposable capacities, distorted probabilities and concave capacities. Math. Soc. Sciences 31 (1996) 19-37
10. Deschamps R., and Gevers L. Leximin and utilitarian rules: A joint characterization. Journal of Economic Theory 17 (1978) 143-163
11. Dubois D. Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence 5 5 (1986) 403-416
12. D. Dubois and H. Fargier. An axiomatic framework for order of magnitude confidence relations. In Proceedings of UAI'04, Banff, CA, 2004.
13. D. Dubois and H. Fargier. Lexicographic refiniments of Sugeno integrals. In K. Mellouli, editor, Symbolic and Quantitative Approaches to Reasoning with Uncertainty (European Conference ECSQARU 2007), volume 4724 of Lecture Notes in Artificial Intelligence, pages 611-622. Springer, 2007.
14. Dubois D., Fargier H., and Prade H. Refinements of the maximin approach to decision-making in a fuzzy environment. Fuzzy Sets Systems 81 1 (1996) 103-122
15. Dubois D., Fargier H., and Prade H. Possibilistic likelihood relations. Proceedings of IPMU'98 (1998), EDK, Paris 1196-1203
16. D. Dubois, H. Prade. Possibility theory as a basis for qualitative decision theory. In Proceedings of the Int. Joint Conf on Artificial Intelligence (IJCAI'95), 20-25 August 1995, pp. 1925-1930.
17. D. Dubois, H. Prade, and R. Sabbadin, Qualitative decision theory with Sugeno integrals. In Proceedings of UAI'98, 1998, pp. 121-128.
18. Dubois D., Prade H., and Sabbadin R. Decision-theoretic foundation of qualitative possibility theory. European Journal of Operations Research 128 (2001) 478-495
19. Fargier H., and Sabbadin R. Qualitative decision under uncertainty: Back to expected utility. Artificial Intelligence 164 (2005) 245-280
20. Grabisch M. The Moebius transform on symmetric ordered structures and its application to capacities on finite sets. Discrete Mathematics 287 (2004) 17-34
21. Grabisch M., and Labreuche C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6 1 (2008) 1-44
22. In: Grabisch M., Murofushi T., and Sugeno M. (Eds). Fuzzy Measures and Integrals - Theory and Applications (2000), Physica Verlag, Heidelberg
23. Greco S., Matarazzo B., and Slowinski R. Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158 2 (2004) 271-292
24. Marichal J.-L. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. I EEE Transactions on Fuzzy Systems 8 6 (2000) 800-807
25. Marichal J.-L. On Sugeno integral as an aggregation function. Fuzzy Sets and Systems 114 3 (2000) 347-365
26. Moulin H. Axioms of Cooperative Decision Making (1988), Wiley, New-York
27. Murofushi T. Lexicographic use of Sugeno integrals and monotonicity conditions. IEEE trans. Fuzzy Systems 9 (2001) 785-794
28. Murofushi T., and Sugeno M. Null sets with respect to fuzzy measures. Proc. 3rd Intern. Fuzzy System Association World Congress (IFSA 1989) (1989), Seattle, Wash 172-175
29. Pap E. Null-Additive Set-Functions (1995), Kluwer Academic, Dordrecht, The Netherlands
30. Rico A., Grabisch M., Labreuche C., and Chateauneuf A. Preference modeling on totally ordered sets by the Sugeno integral. Discrete Applied Mathematics 147 1 (2005) 113-124
31. Sarin R., and Wakker P.P. A simple axiomatization of nonadditive expected utility. Econometrica 60 6 (1992) 1255-1272
32. Schmeidler D. Subjective probability and expected utility without additivity. Econometrica 57 (1989) 571-587
33. Sen A.K. Social Choice Theory. In: Arrow K.J., and Intrilligator M.D. (Eds). Handbook of Mathematical Economics (1986), Elsevier Science Publishers, North-Holland 1073-1181 chapter 22
34. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press, Princeton
35. M. Sugeno, Theory of fuzzy integral and its applications. PhD thesis, Tokyo Institute of Technology, Tokyo, 1974.
36. M. Sugeno, Fuzzy measures and fuzzy integrals: a survey, in: M.M. Gupta, G.N. Saridis, B.R. Gaines (Eds.), Fuzzy Automata and Decision Processes, North-Holland, Amsterdam, 1977, pp. 89-102.
37. Tan S., and Pearl J. Specification and evaluation of preferences under uncertainty. In: Torasso P., Doyle J., and Sandewall E. (Eds). Proceedings of the Int Conf. on Knowledge Representation and Reasoning (KR'94) (1994), Morgan Kaufmann, Bonn Germany 530-539
38. R. Thomason, Desires and defaults: A framework for planning with inferred goals. in: Proceedings of the Int Conf. on Knowledge Representation and Reasoning (KR'00), Breckenridge, CO., USA, 2000, pp. 702-713.
39. Wang Z. The autocontinuity of set function and the fuzzy integral. Journal of Mathematical Analysis and Applications 99 (1984) 195-218
40. Wang Z. Asymptotic structural characteristics of fuzzy measures and their applications. Fuzzy Sets and Systems 16 (1985) 277-290
41. Whalen T. Decision making under uncertainty with various assumptions about available information. IEEE Transactions on Systems, Man and Cybernetics 14 (1984) 888-900
42. Wong S.K.M., Bollmann P., Yao Y.Y., and Burger H.C. Axiomatization of qualitative belief structure. IEEE transactions on SMC 21 34 (1991) 726-734
43. Yager R. Possibilistic decision making. IEEE Transactions on Systems, Man and Cybernetics 9 (1979) 388-392
44. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28