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, Volume 19, Issue 2, pp 421–447 | Cite as

On the Ferrers property of valued interval orders

  • Susana Díaz
  • Bernard De Baets
  • Susana Montes
Original Paper

Abstract

We study the relationship between the Ferrers property and the notion of interval order in the context of valued relations. Given a crisp preference structure without incomparability, the strict preference relation satisfies the Ferrers property if and only if the associated weak preference relation does. These conditions characterize a total interval order. For valued relations the Ferrers property can be written in two different and non-equivalent ways. In this work, we compare these properties by finding the kind of completeness they imply. Moreover, we study whether they still characterize a valued total interval orders.

Keywords

Total interval order Partial interval order Ferrers property Valued relation Completeness 

Mathematics Subject Classification (2000)

62C99 91B08 04A72 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2010

Authors and Affiliations

  • Susana Díaz
    • 1
  • Bernard De Baets
    • 2
  • Susana Montes
    • 1
  1. 1.Dept. Statistics and O. R.University of OviedoOviedoSpain
  2. 2.Dept. of Appl. Math., Biometrics and Process ControlGhent UniversityGhentBelgium

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