Choice, ranking and sorting in fuzzy multiple criteria decision aid

International Series in Operations Research and Management Science

Volumn 78, Issue , 2005, Pages 471-506

  Meyer, Patrick ^a   Roubens, Marc ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Aggregation with fuzzy environment; Choquet integral; Fuzzy choice; Ordinal ordered sorting; TOMASO

Indexed keywords

EID: 78751538727     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: 10.1007/0-387-23081-5_12     Document Type: Chapter

References (35)

1. R. Bisdorff and M. Roubens. On defining and computing fuzzy kernels and l-valued simple graphs. In D. Ruan, P. D’Hondt, P. Govaerts, and E. Kerre, editors, Intelligent Systems and Soft Computing for Nuclear Science and Industry, pages 113–122. World Scientific, Singapore, 1996.
2. D. Botteldooren and A. Verkeyn. Fuzzy models for accumulation of reported community noise annoyance from combined sources. Journal of the Acoustical Society of America, 112:496–1508, 2002.
3. J.P. Brans and P. Vincke. A preference ranking organization method. Management Science, 31:647–656, 1984.
4. G. Choquet. Theory of capacities. Annales de l’Institut Fourier, 5:131–295, 1953.
5. D. Dubois and H. Prade. Weighted minimum and maximum in fuzzy set theory. Information Science, 39:205–210, 1986.
6. J. Fodor, S.A. Orlovski, P. Perny, and M. Roubens. The use of fuzzy preference models in multiple criteria: Choice, ranking and sorting. In D. Dubois and H. Prade, editors, Operations Research and Statistics, volume 5 of Handbooks of Fuzzy Sets, pages 69–101. Kluwer Academic Publishers, Dordrecht, Boston, London, 1998. Chapter 3.
7. J. Fodor, P. Perny, and M. Roubens. Decision making and optimization. In E. Ruspini, P. Bonissone, and W. Pedrycz, editors, Handbook of Fuzzy Computation, pages F.5.1:1–14. Institute of Physics Publication and Oxford University Press, Bristol, 1998. Chapter 5.1.
8. M. Grabisch. K-order additive discrete fuzzy measure and their representation. Fuzzy Sets and Systems, 92:167–189, 1997.
9. M. Grabisch and M. Roubens. Application of the Choquet integral in multicriteria decision making. In M. Grabisch, T. Murofushi, and M. Sugeno, editors, Fuzzy Measures and Integrals, pages 348–374. Physica Verlag, Heidelberg, 2000.
10. S. Greco, B. Matarazzo, and R. Slowinski. Conjoint measurement and rough set approach for multicriteria sorting problems in presence of ordinal criteria. In A. Colorni, M. Paruccini, and B. Roy, editors, A-MCD-A: Aide Multicritère à la Décision (Multiple Criteria Decision Aiding), pages 17–144. Joint Research Centre, Ispra, 2001.European Commission Report, EUR 19808 EN.
11. L. Kitainik. Fuzzy Decision Procedures with Binary Relations. Towards a Unified Theory. Kluwer Academic Publishers, Dordrecht, 1993.
12. J.-L. Marichal. Aggregation Operators for Multicriteria Decision Aid. PhD thesis, Institute of Mathematics, University of Liège, Liège, Belgium, 1998.
13. J.-L. Marichal. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Transactions on Fuzzy Systems, 8:800–807, 2000.
14. J.-L. Marichal. Behavioral analysis of aggregation in multicriteria decision aid. In J. Fodor, B. De Baets, and P. Perny, editors, Preferences and Decisions under Incomplete Knowledge, volume 51 of Studies in Fuzziness and Soft Computing, pages 153–178. Physica Verlag, Heidelberg, 2000.
15. J.-L. Marichal. Aggregation of interacting criteria by means of the discrete Choquet integral. In T. Calvo, G. Mayor, and R. Mesiar, editors, Aggregation Operators: New Trends and Applications, volume 97 of Studies in Fuzziness and Soft Computing, pages 224–244. Physica Verlag, Heidelberg, 2002.
16. J.-L. Marichal and M. Roubens. On a sorting procedure in the presence of qualitative interacting points of view. In J. Chojean and J. Leski, editors, Fuzzy Sets and their Applications, pages 217–230. Silesian University Press, Gliwice, 2001.
17. L.Y. Maystre, J. Pictet, and J. Simos. Méthodes Multicritères ELECTRE. Presses polytechniques et universitaires romandes, Lausanne, 1994.
18. R. Mesiar. Generalizations of k-order additive discrete fuzzy measures. Fuzzy Sets and Systems, 102:423–428, 1999.
19. T. Murofushi and S. Soneda. Techniques for reading fuzzy measures (III): Interaction index. In 9th Fuzzy System Symposium, May 19-21 1993, Sapporo, Japan, pages 693–696, 1993. In Japanese.
20. S.V. Ovchinnikov and M. Roubens. On strict preference relations. Fuzzy Sets and Systems, 43:319–326, 1991.
21. G. Owen. Multilinear extensions of games. Management Science, 18:64–79, 1972.
22. P. Perny. Modélisation, Agrégation et Exploitation de Préférences Floues dans une Problématique de Rangement: Bases Axiomatiques, Procédures et Logiciel. PhD thesis, Université Paris-Dauphine, 1992. LAFORIA document 9.
23. M. Roubens. Ordinal multiattribute sorting and ordering in the presence of interacting points of view. In D. Bouyssou, E. Jacquet-Lagrèze, P. Perny, R. Slowinski, Vanderpooten D., and P. Vincke, editors, Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pages 229–246. Kluwer Academic Publishers, Dordrecht, 2001.
24. M. Roubens and P. Vincke. Fuzzy preferences in an optimisation perspective. In J. Kacprzyk and S.A. Orlovski, editors, Optimization Models Using Fuzzy Sets and Possibility Theory, pages 77–90. D. Reidel, Dordrecht, Boston, Lancaster, Tokyo, 1987.
25. B. Roy. Classement et choix en présence de points de vue multiples (la méthode ELECTRE). Revue d’lnformation et de Recherche Opérationnelle, 8:57–75, 1968.
26. B. Roy. ELECTRE III: Un algorithme de classement fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du Centre d’Etudes en Recherche Opérationnelle, 20(1):3–24, 1978.
27. B. Roy. Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht, 1996.
28. B. Roy and P. Bertier. La méthode ELECTRE II. une application au media planning. In M. Ross, editor, Operational Research 72, pages 291–302. North Holland Publishing Co., 1973.
29. B. Roy and D. Bouyssou. Aide à la décision fondée sur une PAMC de type ELECTRE. Technical Report 69, Université Paris-Dauphine, 1991. Document du LAMSADE.
30. B. Roy and J.-M. Skalka. ELECTRE IS – Aspects méthodologiques et guide d’utilisation. Technical Report 30, Université Paris-Dauphine, 1985. Document du LAMSADE.
31. G. Schmidt and T. Ströhlein. Relations and Graphs – Discrete Mathematics for Computer Scientists. Springer Verlag, Berlin, Heidelberg, New York, 1999.
32. L.S. Shapley. A value for games. In H.W. Kuhn and A.W. Tucker, editors, Contributions to the Theory of Games, Vol. II, volume 28 of Annals of Mathematics Studies, pages 307–317. Princeton University Press, Princeton, NJ, 1953.
33. A. Verkeyn, D. Botteldooren, B. De Baets, and G. De Tre. Modeling annoyance aggregation with Choquet integrals. In B. De Baets, editor, Proceedings of Eurofuse Workshop on Information Systems, September 23-25 2002, Varenna, Italy, pages 259–264, 2002.
34. A. Verkeyn, D. Botteldooren, D. De Baets, and G. de Tre. Sugeno integrals for the modelling of noise annoyance aggregation. In T. Bilgic and et al, editors, IFSA 2003, volume 2715 of Lecture Notes in Artificial Intelligence, pages 277–284. Springer Verlag, Berlin, 2003.
35. P. Wakker. Additive Representations of Preferences: A new Foundation of Decision Analysis. Kluwer Academic Publishers, Dordrecht, Boston, London, 1989.