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Axioms 2017, 6(3), 19; doi:10.3390/axioms6030019

Assigning Numerical Scores to Linguistic Expressions

1
Inarbe (Institute for Advanced Research in Business and Economics), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
2
VIRENA Navarra SL, Beriáin, 31191 Navarra, Spain
3
PRESAD Research Group, BORDA Research Unit, IMUVA, Departamento de Economía Aplicada, Universidad de Valladolid, 47011 Valladolid, Spain
4
InaMat (Institute for Advanced Materials), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Radko Mesiar
Received: 7 June 2017 / Revised: 29 June 2017 / Accepted: 30 June 2017 / Published: 6 July 2017
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
View Full-Text   |   Download PDF [284 KB, uploaded 6 July 2017]   |  

Abstract

In 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. View Full-Text
Keywords: decision making; imprecision; qualitative scales; linguistic expressions; scores; orderings; aggregation decision making; imprecision; qualitative scales; linguistic expressions; scores; orderings; aggregation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Campión, M.J.; Falcó, E.; García-Lapresta, J.L.; Induráin, E. Assigning Numerical Scores to Linguistic Expressions. Axioms 2017, 6, 19.

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