Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) Christophe Labreuche () (TRT - Thales Research & Technology France - THALES)
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The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy. A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme. Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.
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Length: Date of creation: Jul 2008 Date of revision: Publication status: Published, Journal of Mathematical Analysis and applications, 2008, 2, 343, 1080-1097 Handle: RePEc:hal:cesptp:hal-00274267_v1
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00274267/en/ Contact details of provider: Web page: http://hal.archives-ouvertes.fr/
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