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Any complete preference structure without circuit admits an interval representation |
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| Authors: | Moncef Abbas |
| Institution: | (1) Institut de Mathématiques, Département de Recherche Opérationnelle, Université des Sciences et de la Technologie Houari Boumediene, El-Alia, BP 32, 16111 Alger, Algeria;(2) Present address: Service de Mathématiques de la Gestion, Université Libre de Bruxelles, Bd. du triomphe, CP 210/01, 1050 Bruxelles, Belgium |
| Abstract: | This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function. |
| Keywords: | Decision theory preference modelling tolerance interval orders tolerance graphs |
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