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Computing a common preference vector in a complex multi-actor and multi-group decision system in Analytic Hierarchy Process context

Author

Listed:
  • Pietro Amenta

    (University of Sannio)

  • Alessio Ishizaka

    (Faculty of Business & Law, University of Portsmouth)

  • Antonio Lucadamo

    (University of Sannio)

  • Gabriella Marcarelli

    (University of Sannio)

  • Vijay Vyas

    (Faculty of Business & Law, University of Portsmouth)

Abstract

The Analytic Hierarchy Process (hereafter AHP) is a popular multi-criteria decision-making technique. The extant AHP literature usually depicts the geometric mean or the arithmetic mean as a measure of aggregation to process group decisions. However, both these measures are subject to the influence of extreme opinions, and aggregations based on them may not accurately portray the true group preference. In this paper, we propose the Common Priority Vector Procedure, which accentuates the majority group preference and diminishes the influence of extreme individual opinions. The method has been further extended to deal with multi-actor, multi-criteria and multi-group decisions. The development of Common Priority Vector Procedure, presented here, has been motivated by a real case study presented towards the end of the paper.

Suggested Citation

  • Pietro Amenta & Alessio Ishizaka & Antonio Lucadamo & Gabriella Marcarelli & Vijay Vyas, 2020. "Computing a common preference vector in a complex multi-actor and multi-group decision system in Analytic Hierarchy Process context," Annals of Operations Research, Springer, vol. 284(1), pages 33-62, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-019-03258-3
    DOI: 10.1007/s10479-019-03258-3
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    1. Carlo Corradini & Pelin Demirel & Giuliana Battisti, 2016. "Technological diversification within UK’s small serial innovators," Small Business Economics, Springer, vol. 47(1), pages 163-177, June.
    2. Pedro Linares & Sara Lumbreras & Alberto Santamaría & Andrea Veiga, 2016. "How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP," Annals of Operations Research, Springer, vol. 245(1), pages 227-244, October.
    3. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    4. Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
    5. Kun Chen & Gang Kou & J. Michael Tarn & Yan Song, 2015. "Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices," Annals of Operations Research, Springer, vol. 235(1), pages 155-175, December.
    6. László Csató, 2018. "Characterization of an inconsistency ranking for pairwise comparison matrices," Annals of Operations Research, Springer, vol. 261(1), pages 155-165, February.
    7. Colombo, Massimo G. & Piva, Evila & Rossi-Lamastra, Cristina, 2014. "Open innovation and within-industry diversification in small and medium enterprises: The case of open source software firms," Research Policy, Elsevier, vol. 43(5), pages 891-902.
    8. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    9. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    10. Francesco Sandulli & José Fernández-Menéndez & Antonio Rodríguez-Duarte & José López-Sánchez, 2012. "The productivity payoff of information technology in multimarket SMEs," Small Business Economics, Springer, vol. 39(1), pages 99-117, July.
    11. Changsheng Lin & Gang Kou & Daji Ergu, 2013. "An improved statistical approach for consistency test in AHP," Annals of Operations Research, Springer, vol. 211(1), pages 289-299, December.
    12. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 387-400, December.
    13. Valdecy Pereira & Helder Costa, 2015. "Nonlinear programming applied to the reduction of inconsistency in the AHP method," Annals of Operations Research, Springer, vol. 229(1), pages 635-655, June.
    14. 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.
    15. 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.
    16. Gass, S. I. & Rapcsak, T., 2004. "Singular value decomposition in AHP," European Journal of Operational Research, Elsevier, vol. 154(3), pages 573-584, May.
    17. 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.
    18. Xinyi Zhou & Yong Hu & Yong Deng & Felix T. S. Chan & Alessio Ishizaka, 2018. "A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP," Annals of Operations Research, Springer, vol. 271(2), pages 1045-1066, December.
    19. Paul Thaddeus Kazibudzki, 2016. "An examination of performance relations among selected consistency measures for simulated pairwise judgments," Annals of Operations Research, Springer, vol. 244(2), pages 525-544, September.
    20. 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.
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