IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v235y2015i1p155-17510.1007-s10479-015-1997-z.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-015-1997-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-015-1997-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sándor Bozóki & Linda Dezső & Attila Poesz & József Temesi, 2013. "Analysis of pairwise comparison matrices: an empirical research," Annals of Operations Research, Springer, vol. 211(1), pages 511-528, December.
    2. 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.
    3. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    4. Mehdi Ghazanfari & Majid Nojavan, 2004. "Educing Inconsistency In Fuzzy Ahp By Mathematical Programming Models," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 379-391.
    5. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    6. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
    7. Daji Ergu & Gang Kou, 2012. "Questionnaire design improvement and missing item scores estimation for rapid and efficient decision making," Annals of Operations Research, Springer, vol. 197(1), pages 5-23, August.
    8. 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.
    9. Jerónimo Aznar & Francisco Guijarro & José Moreno-Jiménez, 2011. "Mixed valuation methods: a combined AHP-GP procedure for individual and group multicriteria agricultural valuation," Annals of Operations Research, Springer, vol. 190(1), pages 221-238, October.
    10. Jacinto González-Pachón & Carlos Romero, 2007. "Inferring consensus weights from pairwise comparison matrices without suitable properties," Annals of Operations Research, Springer, vol. 154(1), pages 123-132, October.
    11. 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.
    12. Tsuen-Ho Hsu & Li-Chu Hung & Jia-Wei Tang, 2012. "An analytical model for building brand equity in hospitality firms," Annals of Operations Research, Springer, vol. 195(1), pages 355-378, May.
    13. Yi Peng & Yong Shi, 2012. "Editorial: Multiple criteria decision making and operations research," Annals of Operations Research, Springer, vol. 197(1), pages 1-4, August.
    14. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    15. 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.
    16. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    17. András Farkas & Pál Rózsa, 2001. "Data Perturbations of Matrices of Pairwise Comparisons," Annals of Operations Research, Springer, vol. 101(1), pages 401-425, January.
    18. Yael Grushka-Cockayne & Bert De Reyck & Zeger Degraeve, 2008. "An Integrated Decision-Making Approach for Improving European Air Traffic Management," Management Science, INFORMS, vol. 54(8), pages 1395-1409, August.
    19. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    20. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Ignacio J. Navarro & José V. Martí & Víctor Yepes, 2021. "Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices," Mathematics, MDPI, vol. 9(5), pages 1-19, February.
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Alessio Ishizaka & Sajid Siraj, 2020. "Interactive consistency correction in the analytic hierarchy process to preserve ranks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 443-464, December.
    3. Meimei Xia & Jian Chen & Juliang Zhang, 2015. "Multi-criteria decision making based on relative measures," Annals of Operations Research, Springer, vol. 229(1), pages 791-811, June.
    4. Wu, Zhibin & Huang, Shuai & Xu, Jiuping, 2019. "Multi-stage optimization models for individual consistency and group consensus with preference relations," European Journal of Operational Research, Elsevier, vol. 275(1), pages 182-194.
    5. Jiří Mazurek, 2018. "Some notes on the properties of inconsistency indices in pairwise comparisons," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 27-42.
    6. Ardalan Bafahm & Minghe Sun, 2019. "Some Conflicting Results in the Analytic Hierarchy Process," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 465-486, March.
    7. 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.
    8. Virgilio López-Morales & Joel Suárez-Cansino, 2017. "Reliable Intervals Method in Decision-Based Support Models for Group Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 183-204, January.
    9. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
    10. Brunelli, Matteo & Fedrizzi, Michele, 2015. "Boundary properties of the inconsistency of pairwise comparisons in group decisions," European Journal of Operational Research, Elsevier, vol. 240(3), pages 765-773.
    11. Madjid Tavana & Mariya Sodenkamp & Leena Suhl, 2010. "A soft multi-criteria decision analysis model with application to the European Union enlargement," Annals of Operations Research, Springer, vol. 181(1), pages 393-421, December.
    12. 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.
    13. Tomashevskii, I.L., 2015. "Eigenvector ranking method as a measuring tool: Formulas for errors," European Journal of Operational Research, Elsevier, vol. 240(3), pages 774-780.
    14. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez & Alberto Turón, 2020. "The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    15. Zhü, Kèyù, 2014. "Fuzzy analytic hierarchy process: Fallacy of the popular methods," European Journal of Operational Research, Elsevier, vol. 236(1), pages 209-217.
    16. 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.
    17. József Temesi, 2019. "An interactive approach to determine the elements of a pairwise comparison matrix," 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. 27(2), pages 533-549, June.
    18. 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.
    19. Kułakowski, Konrad, 2015. "Notes on order preservation and consistency in AHP," European Journal of Operational Research, Elsevier, vol. 245(1), pages 333-337.
    20. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:155-175:10.1007/s10479-015-1997-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.