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On the Ferrers property of valued interval orders

(2011) TOP. 19(2). p.421-447
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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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Citation

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

Chicago
Diáz, Susana, Bernard De Baets, and Susana Montes. 2011. “On the Ferrers Property of Valued Interval Orders.” TOP 19 (2): 421–447.
APA
Diáz, S., De Baets, B., & Montes, S. (2011). On the Ferrers property of valued interval orders. TOP, 19(2), 421–447.
Vancouver
1.
Diáz S, De Baets B, Montes S. On the Ferrers property of valued interval orders. TOP. 2011;19(2):421–47.
MLA
Diáz, Susana, Bernard De Baets, and Susana Montes. “On the Ferrers Property of Valued Interval Orders.” TOP 19.2 (2011): 421–447. Print.
@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       = {Di{\'a}z, Susana and De Baets, Bernard and Montes, Susana},
  issn         = {1134-5764},
  journal      = {TOP},
  keyword      = {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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