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.
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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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

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