Bipolarization of posets and natural interpolation

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: Thales Research and Technology [Palaiseau] - THALES [France]

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: 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.

Keywords: Interpolation; Choquet integral; Lattice; Bipolar structure (search for similar items in EconPapers)
Date: 2008-07
Note: View the original document on HAL open archive server: https://hal.science/hal-00274267
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Citations: View citations in EconPapers (19)

Published in Journal of Mathematical Analysis and Applications, 2008, 2 (343), pp.1080-1097. ⟨10.1016/j.jmaa.2008.02.008⟩

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Working Paper: Bipolarization of posets and natural interpolation (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00274267

DOI: 10.1016/j.jmaa.2008.02.008

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