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A framework of incorporating confidence levels to deal with uncertainty in pairwise comparisons

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Listed:
  • Georgia Dede

    (Harokopio University)

  • Thomas Kamalakis

    (Harokopio University)

  • Dimosthenis Anagnostopoulos

    (Harokopio University)

Abstract

Pairwise comparison is a key ingredient in multi-criteria decision analysis. The method is based on a set of comparisons conducted by a group of experts, comparing all possible pairs of alternatives involved in the decision process. The outcome is the estimation of weights determining the ranking of alternatives. In this paper, we introduce a new framework for the incorporation of confidence levels in pairwise comparisons, in order to deal with uncertainty issues related to the individual expert judgments. We discuss how the confidence levels can be related to the probability of rank reversal by introducing a theoretical model based on the multivariate normal cumulative distribution function. A comparison between theoretical and numerical results (Monte Carlo simulations), reveals a very good agreement. The proposed framework may provide a very good basis for pairwise comparison extensions aiming to provide further information regarding the accuracy for the evaluation of the final outcome.

Suggested Citation

  • Georgia Dede & Thomas Kamalakis & Dimosthenis Anagnostopoulos, 2022. "A framework of incorporating confidence levels to deal with uncertainty in pairwise comparisons," 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. 30(3), pages 1051-1069, September.
    • Handle: RePEc:spr:cejnor:v:30:y:2022:i:3:d:10.1007_s10100-020-00735-0
    DOI: 10.1007/s10100-020-00735-0
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    References listed on IDEAS

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    1. Siraj, Sajid & Mikhailov, Ludmil & Keane, John A., 2015. "Contribution of individual judgments toward inconsistency in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 242(2), pages 557-567.
    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. Durbach, Ian & Lahdelma, Risto & Salminen, Pekka, 2014. "The analytic hierarchy process with stochastic judgements," European Journal of Operational Research, Elsevier, vol. 238(2), pages 552-559.
    4. Kok, M. & Lootsma, F. A., 1985. "Pairwise-comparison methods in multiple objective programming, with applications in a long-term energy-planning model," European Journal of Operational Research, Elsevier, vol. 22(1), pages 44-55, October.
    5. Beynon, Malcolm, 2002. "DS/AHP method: A mathematical analysis, including an understanding of uncertainty," European Journal of Operational Research, Elsevier, vol. 140(1), pages 148-164, July.
    6. Hamidreza Eskandari & Luis Rabelo, 2007. "Handling Uncertainty In The Analytic Hierarchy Process: A Stochastic Approach," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 177-189.
    7. Sugihara, Kazutomi & Ishii, Hiroaki & Tanaka, Hideo, 2004. "Interval priorities in AHP by interval regression analysis," European Journal of Operational Research, Elsevier, vol. 158(3), pages 745-754, November.
    8. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    9. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    10. Entani, Tomoe & Sugihara, Kazutomi, 2012. "Uncertainty index based interval assignment by Interval AHP," European Journal of Operational Research, Elsevier, vol. 219(2), pages 379-385.
    11. Mikhailov, L., 2004. "A fuzzy approach to deriving priorities from interval pairwise comparison judgements," European Journal of Operational Research, Elsevier, vol. 159(3), pages 687-704, December.
    12. Sajjad Zahir, M., 1991. "Incorporating the uncertainty of decision judgements in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 53(2), pages 206-216, July.
    13. Dede, Georgia & Kamalakis, Thomas & Sphicopoulos, Thomas, 2016. "Theoretical estimation of the probability of weight rank reversal in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 252(2), pages 587-600.
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