129619
20240104102231.0
doi
10.3390/math8060926
sideral
119194
ART-2020-119194
eng
Aguarón, J.
Universidad de Zaragoza
(orcid)0000-0003-3138-7597
The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices
2020
The paper presents the Triads Geometric Consistency Index (T-GCI), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty''s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T-GCI is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index (GCI) and this allows the utilisation of the inconsistency thresholds as well as the properties of the GCI when using the T-GCI. In addition, the decision tools developed for the GCI can be used when working with triads (T-GCI), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures (T-GCI and GCI) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T-GCI. It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult.
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info:eu-repo/grantAgreement/ES/DGA-FEDER/S35-17R
info:eu-repo/semantics/openAccess
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http://creativecommons.org/licenses/by/3.0/es/
2.258
2020
MATHEMATICS
24 / 330 = 0.073
2020
Q1
T1
0.495
2020
Mathematics (miscellaneous)
2020
Q2
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Escobar, M.T.
Universidad de Zaragoza
(orcid)0000-0003-4419-1905
Moreno-Jiménez, J.M.
Universidad de Zaragoza
(orcid)0000-0002-5037-6976
Turón, A.
Universidad de Zaragoza
(orcid)0000-0002-8807-8958
4008
623
Universidad de Zaragoza
Dpto. Estruc.Hª Econ.y Eco.Pb.
Área Métodos Cuant.Econ.Empres
8, 6 (2020), 926 [16 pp.]
Mathematics (Basel)
Mathematics
2227-7390
309641
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