Representation of preferences over a finite scale by a mean operator

Mathematical social sciences

Volumn 52, Issue 2, 2006, Pages 131-151

  Grabisch, Michel ^a  

^a UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

Author keywords

Aggregation of scores; C02; C44; Finite scale; Mean operator; Preference representation; Refinement of scale

Indexed keywords

EID: 33748424022     PISSN: 01654896     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mathsocsci.2006.05.001     Document Type: Article

References (21)

1. Bouyssou D., and Pirlot M. Preferences for multi-attributed alternatives: traces, dominance, and numerical representations. J. Math. Psychol. 48 (2004) 167-185
2. Cauchy, A., 1821. Cours d'Analyse de l'École Royale Polytechnique. Première Partie: Analyse algébrique. Paris.
3. Dubois D., Prade H., and Sabbadin R. Decision-theoretic foundations of qualitative possibility theory. Eur. J. Oper. Res. 128 (2001) 459-478
4. Fargier H., and Sabbadin R. Qualitative decision under uncertainty: back to expected utility. Artif. Intell. 164 (2005) 245-280
5. Fishburn P. Interval Orders, Interval Graphs - A Study of Partially Ordered Sets (1985), J. Wiley and Sons
6. Fodor J. Smooth associative operations on finite ordinal scales. IEEE Trans. Fuzzy Syst. 8 6 (2000) 791-795
7. Grabisch M. The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89 (1996) 445-456
8. Grabisch M. Alternative representations of discrete fuzzy measures for decision making. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997) 587-607
9. Grabisch, M., 2004. Identification of mean aggregation operators on finite scales. Working paper.
10. Grabisch M., Labreuche Ch., and Vansnick J.C. On the extension of pseudo-Boolean functions for the aggregation of interacting bipolar criteria. Eur. J. Oper. Res. 148 (2003) 28-47
11. Krantz D.H., Luce R.D., Suppes P., and Tversky A. Foundations of measurement. Additive and Polynomial Representations vol. 1 (1971), Academic Press
12. Marichal J.L. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Trans. Fuzzy Syst. 8 6 (2000) 800-807
13. Marichal J.L. On Sugeno integral as an aggregation function. Fuzzy Sets Syst. 114 (2000) 347-365
14. Marichal J.L. An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework. IEEE Trans. Fuzzy Syst. 9 1 (2001) 164-172
15. Marichal J.-L., and Mesiar R. Aggregation on finite ordinal scales by scale independent functions. Order 21 (2004) 155-180
16. Marichal J.-L., Mesiar R., and Rückschlossová T. A complete description of comparison meaningful functions. Aequ. Math. 69 (2005) 309-320
17. Mas M., Mayor G., and Torrens J. T-operators and uninorms on a finite totally ordered set. Int. J. Intell. Syst. 14 9 (1999) 909-922
18. Mas M., Monserrat M., and Torrens J. On bisymmetric operators on a finite chain. IEEE Trans. Fuzzy Syst. 11 5 (2003) 647-651
19. Ovchinnikov S. Means on ordered sets. Math. Soc. Sci. 32 (1996) 39-56
20. Rico A., Grabisch M., Labreuche Ch., and Chateauneuf A. Preference modelling on totally ordered sets by the Sugeno integral. Discrete Appl. Math. 147 (2005) 113-124
21. Sugeno, M., 1974. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology.