Kybernetika 51 no. 5, 747-764, 2015

Poset-valued preference relations

Vladimír Janiš, Susana Montes, Branimir Šešelja and Andreja TepavčevićDOI: 10.14736/kyb-2015-5-0747


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.


transitivity, relation, poset, order reversing involutions, weakly orthogonal poset


03G10, 91B08


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