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Ordered sets with interval representation and (m, n)-Ferrers relation

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Date
2008
Dewey
Recherche opérationnelle
Sujet
Preference modelling; Intransitivity; m+ n posets
Journal issue
Annals of Operations Research
Volume
163
Number
1
Publication date
2008
Article pages
177-196
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10479-008-0334-1
URI
https://basepub.dauphine.fr/handle/123456789/2918
Collections
  • LAMSADE : Publications
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Author
Ozturk, Meltem
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that we call “ d-weak orders”, “ d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation.

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