Authors: Janiš, Vladimír
Montes, Susana
Šešelja, Branimir
Tepavčević, Andreja 
Title: Poset-valued preference relations
Journal: Kybernetika
Volume: 51
Issue: 5
First page: 747
Last page: 764
Issue Date: 1-Jan-2015
Rank: M23
ISSN: 0023-5954
DOI: 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.
Keywords: Order reversing involutions | Poset | Relation | Transitivity | Weakly orthogonal poset
Publisher: Academy of Sciences of the Czech Republic, Institute of Information Theory and Automation
Project: Project MTM2010-17844 of the Spanish Ministry of Scienceand Innovation
Grant 1/0297/11 provided by Slovak grant agency VEGA
Development of methods of computation and information processing: theory and applications 

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