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Geometric Compatibility Indexes in a Local AHP-Group Decision Making Context: A Framework for Reducing Incompatibility

Author

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  • 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

This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. An acceptable level of incompatibility between the individual and the group positions will favour the acceptance of the collective position by the individuals. To facilitate the compatibility measurement, the paper utilises four indicators based on log quadratic distances between matrices or vectors which can be employed in accordance with the information that is available from the individual decision makers and from the group. The indicators make it possible to measure compatibility in decision problems, regardless of how the collective position and the priorities are obtained. The paper also presents a theoretical framework and a general, semi-automatic procedure for reducing the incompatibility measured by the four indicators. Using relative variations, the procedure identifies and slightly modifies the judgement of the collective matrix that further improves the indicator. This process is undertaken without modifying the initial information provided by the individuals. A numerical example illustrates the application of the theoretical framework and the procedure.

Suggested Citation

  • Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez & Alberto Turón, 2022. "Geometric Compatibility Indexes in a Local AHP-Group Decision Making Context: A Framework for Reducing Incompatibility," Mathematics, MDPI, vol. 10(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:278-:d:726297
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    References listed on IDEAS

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    1. Alfredo Altuzarra & Pilar Gargallo & José María Moreno-Jiménez & Manuel Salvador, 2019. "Homogeneous Groups of Actors in an AHP-Local Decision Making Context: A Bayesian Analysis," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    2. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    3. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
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    1. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2023. "Reducing incompatibility in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 326(1), pages 1-26, July.

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