The symmetric Sugeno integral

Fuzzy Sets and Systems

Volumn 139, Issue 3, 2003, Pages 473-490

  Grabisch, Michel ^a,b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b THALES   (France)

Author keywords

Fuzzy measure; M bius transform; Ordinal scale; Sugeno integral; Symmetric integral

Indexed keywords

DECISION MAKING; LINEAR ALGEBRA; PROBLEM SOLVING;

NEGATIVE NUMBERS;

FUZZY SETS;

EID: 0141865548     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00499-2     Document Type: Article

References (33)

1. Aigner M. Combinatorial Theory. 1979;Springer, Berlin.
2. Berge C. Principles of Combinatorics. 1971;Academic Press, New York.
3. Cao-Van, B. De Baets, Decomposition of Choquet and Sugeno integrals and the inverse problem, in: 8th Internat. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Madrid, Spain, July 2000, pp. 402-409.
4. Chateauneuf A., Jaffray J.Y. Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math. Social Sci. 17:1989;263-283.
5. Choquet G. Theory of capacities. Annales de I'lnstitut Fourier. 5:1953;131-295.
6. Denneberg D. Non-Additive Measure and Integral. 1994;Kluwer Academic, Dordrecht.
7. Dubois D., Fargier H., Prade H. Beyond min aggregation in multicriteria decision: (ordered) weighted min, discri-min, leximin. Yager R.R., Kacprzyk J. The Ordered Weighted Averaging Operators. Theory and Applications. 1997;181-192 Kluwer Academic Publishers, Dordrecht.
8. Dubois D., Prade H. Possibility Theory. 1988;Plenum Press, New York.
9. Dubois D., Prade H., Sabbadin R. Decision-theoretic foundations of qualitative possibility theory. European J. Oper. Res. 128:2001;459-478.
10. Fishburn P. Multiattribute signed orders. J. Multi-Criteria Decision Anal. 1:1992;3-16.
11. Fuchs L. Partially Ordered Algebraic Systems. 1963;Addison-Wesley, Reading, MA.
12. Grabisch M. k-order additive discrete fuzzy measures and their representation Fuzzy Sets and Systems. 92:1997;167-189.
13. M. Grabisch, On the representation of k -decomposable measures, in: 7th IFSA World Congr., Prague, Czech Republic, June 1997.
14. M. Grabisch, Symmetric and asymmetric fuzzy integrals: the ordinal case, in: 6th Internat. Conf. on Soft Computing (Iizuka'2000), lizuka, Japan, October 2000.
15. M. Grabisch, The Mobius function on symmetric ordered structures and its application to capacities on finite sets, Discrete Math., submitted for publication.
16. M. Grabisch, B. De Baets, J. Fodor, On symmetric pseudo-additions, in: 9th Internat. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'2002), Annecy, France, July 2002, pp. 1349-1355.
17. M. Grabisch, S. Dia, Ch. Labreuche, A multicriteria decision making framework in ordinal context based on Sugeno integral, in: Joint 9th IFSA World Congr. and 20th NAFIPS Internat. Conf., Vancouver, Canada, July 2001.
18. M. Grabisch. Ch. Labreuche, To be symmetric or asymmetric? A dilemma in decision making, in: J. Fodor, B. De Baets, P. Perny (Eds.), Preferences and Decisions under Incomplete Knowledge, Physica Verlag, Wurzburg, 2000, pp. 179-194.
19. Grabisch M., Labreuche Ch. The symmetric and asymmetric Choquet integrals on finite spaces for decision making. Statistical Papers. 43:2002;37-52.
20. P.L. Hammer, R. Holzman, On approximations of pseudo-Boolean functions, RUTCOR Research Report RRR 29-87, State University of New Jersey, 1987.
21. Marichal J.L. On Sugeno integral as an aggregation function. Fuzzy Sets and Systems. 114:2000;347-365.
22. J.L. Marichal, personal communication, 2001.
23. J.L. Marichal, P. Mathonet, E. Tousset, Mesures floues définies sur une échelle ordinale, Working paper, 1996.
24. R. Mesiar, k -order pan-additive discrete fuzzy measures, in: 7th IFSA World Congress, Prague, Czech Republic, June 1997, pp. 488-490.
25. Mesiar R., Komorniková M. Triangular norm-based aggregation of evidence under fuzziness. Bouchon-Meunier B. Aggregation and Fusion of Imperfect Inoformation, Studies in Fuzziness and Soft Computing. 1998;11-35 Physica Verlag, Wurzburg.
26. Schmeidler D. Integral representation without additivity. Proc. Amer. Math. Soc. 97(2):1986;255-261.
27. Schmeidler D. Subjective probability and expected utility without additivity. Econometrica. 57(3):1989;571-587.
28. Shafer G. A Mathematical Theory of Evidence. 1976;Princeton University Press, Princeton, NJ.
29. Šipoš J. Integral with respect to a pre-measure. Math. Slovaca. 29:1979;141-155.
30. Suck R. Factorization and additive decomposition of a weak order. Degreef E., Van Buggenhaut J. Trends in Mathematical Psychology. 1984;347-362 North-Holland, Amsterdam.
31. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.
32. A. Tversky, D. Kahneman, Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncertainty, 1992.
33. Yager R., Rybalov A. Uninorm aggregation operators. Fuzzy Sets and Systems. 80:1996;111-120.