Bipolarization of posets and natural interpolation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article; Proceedings Paper

Grabisch, Michel¹  Labreuche, Christophe² 

[1] Univ Paris 01, Ctr Econ Sorbonne, F-75013 Paris, France

[2] Thales Res & Technol, F-91767 Palaiseau, France

关键词: interpolation;    Choquet integral;    lattice;    bipolar structure;   

DOI  :  10.1016/j.jmaa.2008.02.008

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free