| Autor: |
Philippe Vincke, Marc Pirlot, Moncef Abbas |
| Rok vydání: |
2007 |
| Předmět: |
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| Zdroj: |
Discrete Applied Mathematics. 155(4):429-441 |
| ISSN: |
0166-218X |
| DOI: |
10.1016/j.dam.2006.09.004 |
| Popis: |
Consider a horizontal line in the plane and let @c(A) be a collection of n circles, possibly of different sizes all tangent to the line on the same side. We define the tangent circle graph associated to @c(A) as the intersection graph of the circles. We also define an irreflexive and asymmetric binary relation P on A; the pair (a,b) representing two circles of @c(A) is in P iff the circle associated to a lies to the right of the circle associated to b and does not intersect it. This defines a new nontransitive preference structure that generalizes the semi-order structure. We study its properties and relationships with other well-known order structures, provide a numerical representation and establish a sufficient condition implying that P is transitive. The tangent circle preference structure offers a geometric interpretation of a model of preference relations defined by means of a numerical representation with multiplicative threshold; this representation has appeared in several recently published papers. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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