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

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.

Keywords:

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

Classification:

03G10, 91B08

paper.pdf

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