A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral

European Journal of Operational Research

Volumn 179, Issue 2, 2007, Pages 498-517

  Kojadinovic, Ivan ^a  

^a UNIVERSITÉ DE NANTES   (France)

Author keywords

Aggregation; Bi capacity; Choquet integral; Importance and interaction indices; Multi criteria decision aiding

Indexed keywords

BEHAVIORAL RESEARCH; DIGITAL ARITHMETIC; MATHEMATICAL MODELS; OPERATIONS RESEARCH;

BI-CAPACITY; CHOQUET INTEGRAL; IMPORTANCE AND INTERACTION INDICES; MULTI-CRITERIA DECISION AIDING;

INTEGRAL EQUATIONS;

EID: 33751421504     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2006.03.044     Document Type: Article

References (36)

1. Dubois D., and Prade H. On the use of aggregation operations in information fusion processes. Fuzzy Sets and Systems 142 1 (2004) 143-161
2. Vincke P. Multicriteria Decision-aid (1992), Wiley
3. Grabisch M., Labreuche C., and Vansnick J. On the extension of pseudo-Boolean functions for the aggregation of interacting criteria. European Journal of Operational Research 148 (2003) 28-47
4. Choquet G. Theory of capacities. Annales de l'Institut Fourier 5 (1953) 131-295
5. Grabisch M. Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems 69 (1995) 279-298
6. Marichal J.-L. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Transactions on Fuzzy Systems 8 6 (2000) 800-807
7. Grabisch M., and Labreuche C. Bi-capacities I: Definition, Möbius transform and interaction. Fuzzy Sets and Systems 151 (2005) 211-236
8. Grabisch M., and Labreuche C. Bi-capacities II: The Choquet integral. Fuzzy Sets and Systems 151 (2005) 237-259
9. M. Grabisch, C. Labreuche, Bi-capacities: Towards A Generalization of Cumulative Prospect Theory, working paper, 2005.
10. Labreuche C., and Grabisch M. Generalized Choquet-like aggregation functions for handling bipolar scales. European Journal of Operational Research 172 3 (2006) 931-955
11. M. Grabisch, An axiomatization of the Shapley value and interaction index for games on lattices, in: Second International Conference on Soft Computing and Intelligent Systems and Fifth International Symposium on Advanced Intelligent Systems (SCIS-ISIS 2004), Yokohama, Japan, 2004.
12. F. Lange, M. Grabisch, New axiomatizations of the Shapley interaction index for bi-capacities, in: Joint Fourth EUSFLAT and 11th LFA Conference (EUSFLAT 2005), Barcelona, Spain, 2005, pp. 198-203.
13. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. thesis, Tokyo Institute of Technology, Tokyo, Japan, 1974.
14. Grabisch M., and Roubens M. An axiomatic approach to the concept of interaction among players in cooperative games. International Journal of Game Theory 28 4 (1999) 547-565
15. Grabisch M., Marichal J.-L., and Roubens M. Equivalent representations of set functions. Mathematics of Operations Research 25 2 (2000) 157-178
16. Labreuche C., and Grabisch M. The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets and Systems 137 (2003) 11-16
17. Murofushi T., and Sugeno M. Fuzzy measures and fuzzy integrals. In: Grabisch M., Murofushi T., and Sugeno M. (Eds). Fuzzy Measures and Integrals: Theory and Applications (2000), Physica-Verlag 3-41
18. Denneberg D. Non-additive Measure and Integral (1994), Kluwer Academic, Dordrecht
19. Grabisch M., and Labreuche C. The symmetric and asymmetric Choquet integrals on finite spaces for decision making. Statistical Papers 43 (2002) 37-52
20. Tversky A., and Kahneman D. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5 (1992) 297-323
21. Šipoš J. Integral with respect to a pre-measure. Mathematica Slovaca 29 (1979) 141-155
22. Bilbao J. Cooperative Games on Combinatorial Structures (2000), Kluwer Academic Publishers
23. Felsenthal D., and Machover M. Ternary voting games. International Journal of Game Theory 26 (1997) 335-351
24. S. Greco, B. Matarazzo, R. Slowinski, Bipolar Sugeno and Choquet integrals, in: Seventh Meeting of the EURO Working Group on Fuzzy Sets (EUROFUSE), Varenna, Italy, 2002, pp. 191-196.
25. S. Greco, B. Matarazzo, R. Slowinski, The axiomatic basis of multicriteria noncompensatory preferences, in: Fourth International Workshop on Preferences and Decisions, Trento, Italy, 2003, pp. 81-86.
26. M. Grabisch, C. Labreuche, A general construction for unipolar and bipolar interpolative aggregation, in: Joint Fourth EUSFLAT and 11th LFA Conference (EUSFLAT 2005), Barcelona, Spain, 2005, pp. 916-921.
27. J. Bilbao, J. Fernández, N. Jimńez, J. López, Probabilistic values for bicooperative games, Technical Report, University of Seville, Sevilla, Spain, 2004.
28. I. Kojadinovic, J.-L. Marichal, Entropy of bi-capacities, European Journal of Operational Research, doi:10.1016/j.ejor.2005.10.058.
29. Rota G.-C. On the foundations of combinatorial theory. I. Theory of Möbius functions. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 (1964) 340-368
30. K. Fujimoto, New characterizations of k-additivity and k-monotonicity of bi-capacities, in: Second International Conference on Soft Computing and Intelligent Systems and Fifth International Symposium on Advanced Intelligent Systems (SCIS-ISIS 2004), Yokohama, Japan, 2004.
31. Shapley L.S. A value for n-person games. Contributions to the Theory of Games. Annals of Mathematics Studies, No. 28 vol. 2 (1953), Princeton University Press, Princeton, NJ 307-317
32. Grabisch M. k-Order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92 2 (1997) 167-189
33. T. Murofushi, S. Soneda, Techniques for reading fuzzy measures (iii): Interaction index, in: Ninth Fuzzy System Symposium, Saporo, Japan, 1993, pp. 693-696.
34. Fujimoto K., Kojadinovic I., and Marichal J.-L. Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices. Games and Economic Behavior 55 (2006) 72-99
35. J.-L. Marichal, Aggregation operators for multicriteria decision aid, Ph.D. thesis, University of Liège, Liège, Belgium, 1998.
36. Fujimoto K., and Murofushi T. Some characterizations of k-monotonicity through the bipolar Möbius transform in bi-capacities. Journal of Advanced Computational Intelligence and Intelligent Informatics 9 5 (2005) 484-495