IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v54y2003i7d10.1057_palgrave.jors.2601569.html
   My bibliography  Save this article

Analysis of compatibility between interdependent matrices in ANP

Author

Listed:
  • L C Leung

    (Chinese University of Hong Kong)

  • Y V Hui

    (City University of Hong Kong)

  • M Zheng

    (Fudan University)

Abstract

Analytic network process (ANP) addresses multi-attribute decision-making where attributes exhibit dependencies. A principal characteristic of such problems is that pairwise comparisons are needed for attributes that have interdependencies. We propose that before such comparison matrices are used—in addition to a test that assesses the consistency of a pairwise comparison matrix—a test must also be conducted to assess ‘consistency’ across interdependent matrices. We call such a cross-matrix consistency test as a compatibility test. In this paper, we design a compatibility test for interdependent matrices between two clusters of attributes. We motivate our exposition by addressing compatibility in Sinarchy, a special form of ANP where interdependency exists between the last and next-to-last level. The developed compatibility test is applicable to any pair of interdependent matrices that are a part of an ANP.

Suggested Citation

  • L C Leung & Y V Hui & M Zheng, 2003. "Analysis of compatibility between interdependent matrices in ANP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(7), pages 758-768, July.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:7:d:10.1057_palgrave.jors.2601569
    DOI: 10.1057/palgrave.jors.2601569
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601569
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2601569?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. Schenkerman, Stan, 1994. "Avoiding rank reversal in AHP decision-support models," European Journal of Operational Research, Elsevier, vol. 74(3), pages 407-419, May.
    2. Joaquin Pérez, 1995. "Some Comments on Saaty's AHP," Management Science, INFORMS, vol. 41(6), pages 1091-1095, June.
    3. 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.
    4. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    5. Leung, Lawrence C. & Cao, Dong, 2001. "On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 39-49, July.
    6. Vargas, Luis G., 1994. "Reply to Schenkerman's avoiding rank reversal in AHP decision support models," European Journal of Operational Research, Elsevier, vol. 74(3), pages 420-425, May.
    7. Watson, SR, 1982. "Assesing Attribute Weights," Omega, Elsevier, vol. 10(6), pages 582-583.
    8. Belton, Valerie & Gear, Tony, 1985. "The legitimacy of rank reversal--A comment," Omega, Elsevier, vol. 13(3), pages 143-144.
    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. Thomas L. Saaty, 1994. "How to Make a Decision: The Analytic Hierarchy Process," Interfaces, INFORMS, vol. 24(6), pages 19-43, December.
    11. Schoner, Bertram & Wedley, William C. & Choo, Eng Ung, 1993. "A unified approach to AHP with linking pins," European Journal of Operational Research, Elsevier, vol. 64(3), pages 384-392, February.
    12. 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. L C Leung & K C Lam & D Cao, 2006. "Implementing the balanced scorecard using the analytic hierarchy process & the analytic network process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 682-691, June.
    2. Chen, Shih-Hsin & Lin, Wei-Ting, 2018. "Analyzing determinants for promoting emerging technology through intermediaries by using a DANP-based MCDA framework," Technological Forecasting and Social Change, Elsevier, vol. 131(C), pages 94-110.
    3. Cooper, Orrin & Yavuz, Idil, 2016. "Linking validation: A search for coherency within the Supermatrix," European Journal of Operational Research, Elsevier, vol. 252(1), pages 232-245.

    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. Leung, Lawrence C. & Cao, Dong, 2001. "On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 39-49, July.
    2. 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.
    3. Majumdar, Abhijit & Tiwari, Manoj Kumar & Agarwal, Aastha & Prajapat, Kanika, 2021. "A new case of rank reversal in analytic hierarchy process due to aggregation of cost and benefit criteria," Operations Research Perspectives, Elsevier, vol. 8(C).
    4. 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.
    5. Rosenbloom, E. S., 1997. "A probabilistic interpretation of the final rankings in AHP," European Journal of Operational Research, Elsevier, vol. 96(2), pages 371-378, January.
    6. Weck, M. & Klocke, F. & Schell, H. & Ruenauver, E., 1997. "Evaluating alternative production cycles using the extended fuzzy AHP method," European Journal of Operational Research, Elsevier, vol. 100(2), pages 351-366, July.
    7. Kumar, N. Vinod & Ganesh, L. S., 1996. "A simulation-based evaluation of the approximate and the exact eigenvector methods employed in AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 656-662, December.
    8. M Tavana, 2006. "A priority assessment multi-criteria decision model for human spaceflight mission planning at NASA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1197-1215, October.
    9. Suwignjo, P. & Bititci, U. S & Carrie, A. S, 2000. "Quantitative models for performance measurement system," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 231-241, March.
    10. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    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. Lai, S-K., 1995. "A preference-based interpretation of AHP," Omega, Elsevier, vol. 23(4), pages 453-462, August.
    13. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    14. 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.
    15. 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.
    16. Wedley, William C. & Choo, Eng Ung & Schoner, Bertram, 2001. "Magnitude adjustment for AHP benefit/cost ratios," European Journal of Operational Research, Elsevier, vol. 133(2), pages 342-351, January.
    17. Williams, Michael L. & Dennis, Alan R. & Stam, Antonie & Aronson, Jay E., 2007. "The impact of DSS use and information load on errors and decision quality," European Journal of Operational Research, Elsevier, vol. 176(1), pages 468-481, January.
    18. Millet, Ido & Saaty, Thomas L., 2000. "On the relativity of relative measures - accommodating both rank preservation and rank reversals in the AHP," European Journal of Operational Research, Elsevier, vol. 121(1), pages 205-212, February.
    19. 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.
    20. Azzopardi, Ernest & Nash, Robert, 2013. "A critical evaluation of importance–performance analysis," Tourism Management, Elsevier, vol. 35(C), pages 222-233.

    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:pal:jorsoc:v:54:y:2003:i:7:d:10.1057_palgrave.jors.2601569. 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.palgrave-journals.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.