Poset-valued preference relations

Vladimír Janiš; Susana Montes; Branimir Šešelja; Andreja Tepavčević

Kybernetika (2015)

  • Volume: 51, Issue: 5, page 747-764
  • ISSN: 0023-5954

Abstract

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In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.

How to cite

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Janiš, Vladimír, et al. "Poset-valued preference relations." Kybernetika 51.5 (2015): 747-764. <http://eudml.org/doc/276117>.

@article{Janiš2015,
abstract = {In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.},
author = {Janiš, Vladimír, Montes, Susana, Šešelja, Branimir, Tepavčević, Andreja},
journal = {Kybernetika},
keywords = {relation; poset; order reversing involutions; weakly orthogonal poset; transitivity},
language = {eng},
number = {5},
pages = {747-764},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Poset-valued preference relations},
url = {http://eudml.org/doc/276117},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Janiš, Vladimír
AU - Montes, Susana
AU - Šešelja, Branimir
AU - Tepavčević, Andreja
TI - Poset-valued preference relations
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 747
EP - 764
AB - In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.
LA - eng
KW - relation; poset; order reversing involutions; weakly orthogonal poset; transitivity
UR - http://eudml.org/doc/276117
ER -

References

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