New axiomatizations of the Shapley interaction index for bi-capacities
AbstractBi-capacities are a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours. After a short presentation of the basis structure, we introduce the Shapley value and the interaction index for capacities. Afterwards, the case of bi-capacities is studied with new axiomatizations of the interaction index.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00625355.
Date of creation: 2011
Date of revision:
Publication status: Published, Fuzzy Sets and Systems, 2011, 64-75
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00625355
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Marc Roubens & Michel Grabisch, 1999.
"An axiomatic approach to the concept of interaction among players in cooperative games,"
International Journal of Game Theory, Springer,
Springer, vol. 28(4), pages 547-565.
- Grabisch, M. & Roubens, M., 1998. "An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games," Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et 9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
- Christophe Labreuche & Michel Grabisch, 2006.
"Axiomatization of the Shapley value and power index for bi-cooperative games,"
Cahiers de la Maison des Sciences Economiques, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1)
b06023, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Christophe Labreuche & Michel Grabisch, 2006. "Axiomatisation of the Shapley value and power index for bi-cooperative games," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00113340, HAL.
- MoshÃŠ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, Springer, vol. 26(3), pages 335-351.
- Kojadinovic, Ivan, 2007. "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, Elsevier, Elsevier, vol. 179(2), pages 498-517, June.
- Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
- JesÃºs Mario Bilbao & Julio R. FernÃ¡ndez & Nieves JimÃ©nez & Jorge JesÃºs LÃ³pez, 2004. "The Shapley value for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/56, Centro de Estudios Andaluces.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.