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On the Ferrers property of valued interval orders

Susana Diáz, Bernard De Baets (UGent) and Susana Montes
(2011) TOP. 19(2). p.421-447
Author
Organization
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
Partial interval order, Total interval order, Ferrers property, Valued relation, Completeness, FUZZY PREFERENCE STRUCTURES, BINARY RELATIONS, T-NORMS, TRANSITIVITY, DIMENSION

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Please use this url to cite or link to this publication:

MLA
Diáz, Susana, et al. “On the Ferrers Property of Valued Interval Orders.” TOP, vol. 19, no. 2, 2011, pp. 421–47, doi:10.1007/s11750-010-0134-z.
APA
Diáz, S., De Baets, B., & Montes, S. (2011). On the Ferrers property of valued interval orders. TOP, 19(2), 421–447. https://doi.org/10.1007/s11750-010-0134-z
Chicago author-date
Diáz, Susana, Bernard De Baets, and Susana Montes. 2011. “On the Ferrers Property of Valued Interval Orders.” TOP 19 (2): 421–47. https://doi.org/10.1007/s11750-010-0134-z.
Chicago author-date (all authors)
Diáz, Susana, Bernard De Baets, and Susana Montes. 2011. “On the Ferrers Property of Valued Interval Orders.” TOP 19 (2): 421–447. doi:10.1007/s11750-010-0134-z.
Vancouver
1.
Diáz S, De Baets B, Montes S. On the Ferrers property of valued interval orders. TOP. 2011;19(2):421–47.
IEEE
[1]
S. Diáz, B. De Baets, and S. Montes, “On the Ferrers property of valued interval orders,” TOP, vol. 19, no. 2, pp. 421–447, 2011.
@article{2135706,
  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.}},
  author       = {{Diáz, Susana and De Baets, Bernard and Montes, Susana}},
  issn         = {{1134-5764}},
  journal      = {{TOP}},
  keywords     = {{Partial interval order,Total interval order,Ferrers property,Valued relation,Completeness,FUZZY PREFERENCE STRUCTURES,BINARY RELATIONS,T-NORMS,TRANSITIVITY,DIMENSION}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{421--447}},
  title        = {{On the Ferrers property of valued interval orders}},
  url          = {{http://dx.doi.org/10.1007/s11750-010-0134-z}},
  volume       = {{19}},
  year         = {{2011}},
}
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