Campión Arrastia, María JesúsFalcó Díaz de Cerio, EdurneGarcía Lapresta, JoséInduráin Eraso, Esteban2017-11-152017-11-1520172075-168010.3390/axioms6030019https://academica-e.unavarra.es/handle/2454/26182In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed.17 p.application/pdfeng© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Decision makingImprecisionQualitative scalesLinguistic expressionsScoresOrderingsAggregationinfo:eu-repo/semantics/articleAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess