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AHP-Group Decision Making Based on Consistency

Author

Listed:
  • Juan Aguarón

    (Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain)

  • María Teresa Escobar

    (Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain)

  • José María Moreno-Jiménez

    (Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain)

  • Alberto Turón

    (Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain)

Abstract

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

Suggested Citation

  • Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez & Alberto Turón, 2019. "AHP-Group Decision Making Based on Consistency," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:242-:d:211961
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    References listed on IDEAS

    as
    1. Manuel Salvador & Alfredo Altuzarra & Pilar Gargallo & José María Moreno-Jiménez, 2015. "A Bayesian Approach to Maximising Inner Compatibility in AHP-Systemic Decision Making," Group Decision and Negotiation, Springer, vol. 24(4), pages 655-673, July.
    2. Alberto Turón & Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2019. "A Decision Support System and Visualisation Tools for AHP-GDM," International Journal of Decision Support System Technology (IJDSST), IGI Global, vol. 11(1), pages 1-19, January.
    3. María Teresa Escobar & José María Moreno-jiménez, 2007. "Aggregation of Individual Preference Structures in Ahp-Group Decision Making," Group Decision and Negotiation, Springer, vol. 16(4), pages 287-301, July.
    4. Ramanathan, R. & Ganesh, L. S., 1994. "Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages," European Journal of Operational Research, Elsevier, vol. 79(2), pages 249-265, December.
    5. Aguaron, Juan & Escobar, Maria Teresa & Moreno-Jimenez, Jose Maria, 2003. "Consistency stability intervals for a judgement in AHP decision support systems," European Journal of Operational Research, Elsevier, vol. 145(2), pages 382-393, March.
    6. Altuzarra, Alfredo & Moreno-Jimenez, Jose Maria & Salvador, Manuel, 2007. "A Bayesian priorization procedure for AHP-group decision making," European Journal of Operational Research, Elsevier, vol. 182(1), pages 367-382, October.
    7. Golany, B. & Kress, M., 1993. "A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices," European Journal of Operational Research, Elsevier, vol. 69(2), pages 210-220, September.
    8. Escobar, M. T. & Aguaron, J. & Moreno-Jimenez, J. M., 2004. "A note on AHP group consistency for the row geometric mean priorization procedure," European Journal of Operational Research, Elsevier, vol. 153(2), pages 318-322, March.
    9. Forman, Ernest & Peniwati, Kirti, 1998. "Aggregating individual judgments and priorities with the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 108(1), pages 165-169, July.
    10. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2016. "The precise consistency consensus matrix in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 245(1), pages 245-259, October.
    11. José María Moreno-Jiménez & Manuel Salvador & Pilar Gargallo & Alfredo Altuzarra, 2016. "Systemic decision making in AHP: a Bayesian approach," Annals of Operations Research, Springer, vol. 245(1), pages 261-284, October.
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