The duality between the anti-exchange closure operators and the path independent choice operators on a finite set, - HAL Access content directly
Journal articles Mathematical Social Sciences Year : 2001

The duality between the anti-exchange closure operators and the path independent choice operators on a finite set,

Abstract

In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results concerning the "ordinal" representations of path independent choice functions from the theory of anti-exchange closure operators.
Dans cet article, nous montrons que la correspondance découverte par Koshevoy ([18]) et Johnson et Dean ([15],[16]) entre les fermetures « anti-échanges » et les fonctions de choix « chemin-indépendantes » est une dualité entre les deux demi-treillis de ces applications. Nous utilisons cette dualité pour obtenir des résultats sur la représentation des fonctions de choix « chemin-indépendantes » au moyen de la théorie des fermetures « anti-échanges ».
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Dates and versions

halshs-00214289, version 1 (23-01-2008)

Identifiers

  • HAL Id : halshs-00214289 , version 1

Cite

Bernard Monjardet, Raderanirina Vololonirina. The duality between the anti-exchange closure operators and the path independent choice operators on a finite set,. Mathematical Social Sciences, 2001, 41 (2), pp.131-150. ⟨halshs-00214289⟩
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