Geodesic
Poset-valued preference relations
Kybernetika, Tome 51 (2015) no. 5, pp. 747-764.

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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.
DOI : 10.14736/kyb-2015-5-0747
Classification : 03G10, 91B08
Keywords: relation; poset; order reversing involutions; weakly orthogonal poset; transitivity 
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     title = {Poset-valued preference relations},
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Janiš, Vladimír; Montes, Susana; Šešelja, Branimir; Tepavčević, Andreja. Poset-valued preference relations. Kybernetika, Tome 51 (2015) no. 5, pp. 747-764. doi : 10.14736/kyb-2015-5-0747. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-5-0747/

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