The Choquet integral with respect to a level dependent capacity

Fuzzy Sets and Systems

Volumn 175, Issue 1, 2011, Pages 1-35

  Greco, Salvatore ^a   Matarazzo, Benedetto ^a   Giove, Silvio ^b  

^a UNIVERSITY OF CATANIA   (Italy)

^b CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

Aggregation functions; Choquet integral; Cumulative Prospect Theory functional; Level dependent bicapacity; Level dependent capacity; OWA; Sugeno integral

Indexed keywords

AGGREGATION FUNCTIONS; CHOQUET INTEGRAL; CUMULATIVE PROSPECT THEORY; LEVEL DEPENDENT BICAPACITY; LEVEL DEPENDENT CAPACITY; OWA; SUGENO INTEGRALS;

INTEGRAL EQUATIONS;

EID: 79956273878     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.03.012     Document Type: Article

References (25)

1. S. Angilella, S. Greco, F. Lamantia, and B. Matarazzo Assessing non-additive utility for multicriteria decision aid European Journal of Operational Research 158 2004 734 744
2. S.H. Chew, and L.G. Epstein A unifying approach to axiomatic non-expected utility theories Journal of Economic Theory 49 1989 207 240
3. G. Choquet Theory of capacities Annales de l' Institut Fourier 5 1954 131 295
4. J. Figueira, S. Greco, M. Ehrgott (Eds.), Multiple Criteria Decision Analysis, Springer, New York, 2005.
5. M. Grabisch On equivalence classes of fuzzy connectives: the case of fuzzy integrals IEEE Transactions on Fuzzy Systems 3 1995 96 109
6. M. Grabisch The application of fuzzy integrals in multicriteria decision making European Journal of Operational Research 89 1996 445 456 (Pubitemid 126386777)
7. M. Grabisch k-Order additive discrete fuzzy measures and their representation Fuzzy Sets and Systems 92 1997 167 189
8. M. Grabisch, and Ch. Labreuche Fuzzy measures and integrals in MCDA J. Figueira, S. Greco, M. Ehrgott, Multiple Criteria Decision Analysis 2005 Springer New York 563 608
9. M. Grabisch, and Ch. Labreuche Bi-capacities - Part I: definition, Möbius transform and interaction Fuzzy Sets and Systems 151 2005 211 236 (Pubitemid 40231849)
10. M. Grabisch, and Ch. Labreuche Bi-capacities - Part II: the Choquet integral Fuzzy Sets and Systems 151 2005 237 259
11. M. Grabisch, Ch. Labreuche, Capacities on lattices and k-ary capacities, in: 3rd International Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2003), Zittau, Germany, September 2003, pp. 304-307.
12. S. Greco, B. Matarazzo, R. Slowinski, Bipolar Sugeno and Choquet integrals, in: B. De Baets, J. Fodor, G. Pasi (Eds.), EUROWorking Group on Fuzzy Sets, Workshop on Informations Systems (EUROFUSE 2002), Varenna, Italy, September 2002, pp. 191-196.
13. J.R. Green, and B. Jullien Ordinal independence in nonlinear utility theory Journal of Risk and Uncertainty 1 1988 355 387
14. M. Li Calzi Valuations of the measure representation approach Journal of Mathematical Economics 29 1998 255 269
15. J.L. Marichal An axiomatic approach of the discrete sugeno integral as a tool to aggregate interacting criteria in a qualitative framework IEEE Transactions on Fuzzy Systems 9 1 2001 164 172
16. J.L. Marichal, and M. Roubens Determination of weights of interactive criteria from a reference set European Journal of Operational Research 124 2000 641 650
17. T. Murofushi, Techniques for reading fuzzy measures (I): the Shapley value with respect to a fuzzy measure, in: 2nd Fuzzy Workshop, Nagaoka, Japan, October 1992, pp. 39-48 (in Japanese).
18. T. Murofushi, S. Soneda, Techniques for reading fuzzy measures (III): interaction index, in: 9th Fuzzy System Symposium, Sapporo, Japan, May 1993, pp. 693-696 (in Japanese).
19. T. Murofushi, and M. Sugeno Some quantities represented by the Choquet integral Fuzzy Sets and Systems 56 1993 229 235
20. U. Segal Anticipated utility: a measure representation approach Annals of Operations Research 19 1989 359 373
21. L.S. Shapley A value for n-person games H.W. Kuhn, A.W. Tucker, Contributions to the Theory of Games, Vol. II, Annals of Mathematics Studies vol. 28 1953 Princeton University Press Princeton, NJ 307 317
22. J. Šipoš Integral with respect to pre-measure Mathematica Slovaca 29 1979 141 155
23. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.
24. A. Tversky, and D. Kahneman Advances in prospect theory: cumulative representation of uncertainty Journal of Risk and Uncertainty 5 1992 297 323
25. R.R. Yager On ordered weighted averaging aggregation operators in multicriteria decision making IEEE Transactions on Systems, Man and Cybernetics 18 1988 183 190