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Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices

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  • Kun Chen
  • Gang Kou
  • J. Michael Tarn
  • Yan Song

Abstract

Missing values and inconsistency of pairwise comparison matrices (PCM) in AHP are tackled with different methods in extant studies. In this article, we prove that connecting path method (CPM), which is a well-known approach of estimating missing judgments, also guarantees minimal geometric consistency index, and only involves elementary connecting paths by unraveling its connection with logarithmic least square method. The formal proofs suggest that CPM alone is sufficient to fix both missing judgments and inconsistency of PCM in AHP. Based on this well grounded merit, a procedure is proposed to improve consistency for incomplete PCM. The validity of the proposed procedure is illustrated by classical examples, and its advantages over other consistency improving approaches are also discussed in detail. Copyright Springer Science+Business Media New York 2015

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  • 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.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:155-175:10.1007/s10479-015-1997-z
    DOI: 10.1007/s10479-015-1997-z
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    Cited by:

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    3. 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.
    4. Abastante, Francesca & Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio & Lami, Isabella M., 2018. "Choice architecture for architecture choices: Evaluating social housing initiatives putting together a parsimonious AHP methodology and the Choquet integral," Land Use Policy, Elsevier, vol. 78(C), pages 748-762.
    5. Ágoston, Kolos Csaba & Csató, László, 2024. "A lexicographically optimal completion for pairwise comparison matrices with missing entries," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1078-1086.
    6. Idil Yavuz & Orrin Cooper, 2017. "A dynamic clustering method to improve the coherency of an ANP Supermatrix," Annals of Operations Research, Springer, vol. 254(1), pages 507-531, July.
    7. 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.
    8. Liu, Fang & Zou, Shu-Cai & Li, Qing, 2020. "Deriving priorities from pairwise comparison matrices with a novel consistency index," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    9. Matteo Brunelli, 2017. "Studying a set of properties of inconsistency indices for pairwise comparisons," Annals of Operations Research, Springer, vol. 248(1), pages 143-161, January.
    10. Tekile, Hailemariam Abebe & Brunelli, Matteo & Fedrizzi, Michele, 2023. "A numerical comparative study of completion methods for pairwise comparison matrices," Operations Research Perspectives, Elsevier, vol. 10(C).

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