IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v161y2014i3d10.1007_s10957-012-0223-2.html
   My bibliography  Save this article

Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

Author

Listed:
  • Daji Ergu

    (University of Electronic Science and Technology of China
    Southwest University for Nationalities)

  • Gang Kou

    (University of Electronic Science and Technology of China)

  • János Fülöp

    (Hungarian Academy of Sciences)

  • Yong Shi

    (University of Nebraska at Omaha
    Chinese Academy of Sciences)

Abstract

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.

Suggested Citation

  • Daji Ergu & Gang Kou & János Fülöp & Yong Shi, 2014. "Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 980-993, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-012-0223-2
    DOI: 10.1007/s10957-012-0223-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0223-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-0223-2?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. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
    2. 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.
    3. Saaty, Thomas L., 1990. "How to make a decision: The analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 48(1), pages 9-26, September.
    4. S. Lipovetsky, 2009. "Global Priority Estimation in Multiperson Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 77-91, January.
    5. Patrick T. Harker & Luis G. Vargas, 1987. "The Theory of Ratio Scale Estimation: Saaty's Analytic Hierarchy Process," Management Science, INFORMS, vol. 33(11), pages 1383-1403, November.
    6. Yi Peng & Gang Kou & Guoxun Wang & Wenshuai Wu & Yong Shi, 2011. "Ensemble Of Software Defect Predictors: An Ahp-Based Evaluation Method," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 187-206.
    7. Sándor Bozóki & János Fülöp & Attila Poesz, 2011. "On pairwise comparison matrices that can be made consistent by the modification of a few elements," 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. 19(2), pages 157-175, June.
    8. 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.
    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. L. Sun & B. S. Greenberg, 2006. "Multicriteria Group Decision Making: Optimal Priority Synthesis from Pairwise Comparisons," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 317-339, August.
    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. Garbuzova-Schlifter, Maria & Madlener, Reinhard, 2016. "AHP-based risk analysis of energy performance contracting projects in Russia," Energy Policy, Elsevier, vol. 97(C), pages 559-581.

    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. 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.
    2. Wenshuai Wu & Gang Kou, 2016. "A group consensus model for evaluating real estate investment alternatives," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-10, December.
    3. Kang Xu & Jiuping Xu, 2020. "A direct consistency test and improvement method for the analytic hierarchy process," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 359-388, September.
    4. 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.
    5. 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.
    6. 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.
    7. Muhammad Ikram & Qingyu Zhang & Robert Sroufe, 2020. "Developing integrated management systems using an AHP‐Fuzzy VIKOR approach," Business Strategy and the Environment, Wiley Blackwell, vol. 29(6), pages 2265-2283, September.
    8. Carmone, Frank J. & Kara, Ali & Zanakis, Stelios H., 1997. "A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP," European Journal of Operational Research, Elsevier, vol. 102(3), pages 538-553, November.
    9. Paul J. Componation & Dawn R. Utley & Robert L. Armacost, 1999. "Prioritizing components of concurrent engineering programs to support new product development," Systems Engineering, John Wiley & Sons, vol. 2(3), pages 168-176.
    10. Dong, Yucheng & Hong, Wei-Chiang & Xu, Yinfeng & Yu, Shui, 2013. "Numerical scales generated individually for analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 229(3), pages 654-662.
    11. Mehmet Yüksel, 2019. "A Model Proposal for the Evaluation of Chemistry Education in the Context of Learning Environment," Asian Journal of Education and Training, Asian Online Journal Publishing Group, vol. 5(3), pages 488-494.
    12. 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.
    13. Sarah Ben Amor & Fateh Belaid & Ramzi Benkraiem & Boumediene Ramdani & Khaled Guesmi, 2023. "Multi-criteria classification, sorting, and clustering: a bibliometric review and research agenda," Annals of Operations Research, Springer, vol. 325(2), pages 771-793, June.
    14. L. N. Pradeep Kumar Rallabandi & Ravindranath Vandrangi & Subba Rao Rachakonda, 2016. "Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-19, June.
    15. Fahrettin Eldemir & Ismail Onden, 2016. "Geographical Information Systems and Multicriteria Decisions Integration Approach for Hospital Location Selection," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 975-997, September.
    16. Bentes, Alexandre Veronese & Carneiro, Jorge & da Silva, Jorge Ferreira & Kimura, Herbert, 2012. "Multidimensional assessment of organizational performance: Integrating BSC and AHP," Journal of Business Research, Elsevier, vol. 65(12), pages 1790-1799.
    17. Sadeghi, Mehdi & Ameli, Ahmad, 2012. "An AHP decision making model for optimal allocation of energy subsidy among socio-economic subsectors in Iran," Energy Policy, Elsevier, vol. 45(C), pages 24-32.
    18. Zhü, Kèyù, 2014. "Fuzzy analytic hierarchy process: Fallacy of the popular methods," European Journal of Operational Research, Elsevier, vol. 236(1), pages 209-217.
    19. Lee, Mindy & Pham, Hoang & Zhang, Xuemei, 1999. "A methodology for priority setting with application to software development process," European Journal of Operational Research, Elsevier, vol. 118(2), pages 375-389, October.
    20. 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.

    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:joptap:v:161:y:2014:i:3:d:10.1007_s10957-012-0223-2. 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.