000129619 001__ 129619 000129619 005__ 20240104102231.0 000129619 0247_ $$2doi$$a10.3390/math8060926 000129619 0248_ $$2sideral$$a119194 000129619 037__ $$aART-2020-119194 000129619 041__ $$aeng 000129619 100__ $$0(orcid)0000-0003-3138-7597$$aAguarón, J.$$uUniversidad de Zaragoza 000129619 245__ $$aThe Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices 000129619 260__ $$c2020 000129619 5060_ $$aAccess copy available to the general public$$fUnrestricted 000129619 5203_ $$aThe 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. 000129619 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/S35-17R 000129619 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000129619 590__ $$a2.258$$b2020 000129619 591__ $$aMATHEMATICS$$b24 / 330 = 0.073$$c2020$$dQ1$$eT1 000129619 592__ $$a0.495$$b2020 000129619 593__ $$aMathematics (miscellaneous)$$c2020$$dQ2 000129619 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000129619 700__ $$0(orcid)0000-0003-4419-1905$$aEscobar, M.T.$$uUniversidad de Zaragoza 000129619 700__ $$0(orcid)0000-0002-5037-6976$$aMoreno-Jiménez, J.M.$$uUniversidad de Zaragoza 000129619 700__ $$0(orcid)0000-0002-8807-8958$$aTurón, A.$$uUniversidad de Zaragoza 000129619 7102_ $$14008$$2623$$aUniversidad de Zaragoza$$bDpto. Estruc.Hª Econ.y Eco.Pb.$$cÁrea Métodos Cuant.Econ.Empres 000129619 773__ $$g8, 6 (2020), 926 [16 pp.]$$pMathematics (Basel)$$tMathematics$$x2227-7390 000129619 8564_ $$s309641$$uhttps://zaguan.unizar.es/record/129619/files/texto_completo.pdf$$yVersión publicada 000129619 8564_ $$s2444047$$uhttps://zaguan.unizar.es/record/129619/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000129619 909CO $$ooai:zaguan.unizar.es:129619$$particulos$$pdriver 000129619 951__ $$a2024-01-04-09:05:56 000129619 980__ $$aARTICLE