IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1873-d436577.html
   My bibliography  Save this article

On the Geometric Mean Method for Incomplete Pairwise Comparisons

Author

Listed:
  • Konrad Kułakowski

    (Department of Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland)

Abstract

One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step.

Suggested Citation

  • Konrad Kułakowski, 2020. "On the Geometric Mean Method for Incomplete Pairwise Comparisons," Mathematics, MDPI, vol. 8(11), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1873-:d:436577
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1873/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/1873/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Doumpos, Michalis & Figueira, José Rui, 2019. "A multicriteria outranking approach for modeling corporate credit ratings: An application of the Electre Tri-nC method," Omega, Elsevier, vol. 82(C), pages 166-180.
    Full references (including those not matched with items on IDEAS)

    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. Julio Cezar Soares Silva & Diogo Ferreira de Lima Silva & Luciano Ferreira & Adiel Teixeira de Almeida-Filho, 2022. "A dominance-based rough set approach applied to evaluate the credit risk of sovereign bonds," 4OR, Springer, vol. 20(1), pages 139-164, March.
    2. Jaspreet Kaur & Madhu Vij & Ajay Kumar Chauhan, 2023. "Signals influencing corporate credit ratings—a systematic literature review," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(1), pages 91-114, March.
    3. Mohammad Mahdi Mousavi & Jamal Ouenniche & Kaoru Tone, 2023. "A dynamic performance evaluation of distress prediction models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 756-784, July.
    4. Davoodi, Shayan & Fereydooni, Ali & Rastegar, Mohammad Ali, 2024. "Can portfolio construction considering ESG still gain high profits?," Research in International Business and Finance, Elsevier, vol. 67(PA).
    5. Carlo Alberto Magni & Stefano Malagoli & Andrea Marchioni & Giovanni Mastroleo, 2020. "Rating firms and sensitivity analysis," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(12), pages 1940-1958, December.
    6. Jiapeng Liu & Miłosz Kadziński & Xiuwu Liao & Xiaoxin Mao, 2021. "Data-Driven Preference Learning Methods for Value-Driven Multiple Criteria Sorting with Interacting Criteria," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 586-606, May.
    7. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    8. Marco Corazza & Giovanni Fasano & Stefania Funari & Riccardo Gusso, 2021. "MURAME parameter setting for creditworthiness evaluation: data-driven optimization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 295-339, June.
    9. Pranith K. Roy & Krishnendu Shaw, 2023. "A credit scoring model for SMEs using AHP and TOPSIS," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 372-391, January.
    10. Pranith Kumar Roy & Krishnendu Shaw & Alessio Ishizaka, 2023. "Developing an integrated fuzzy credit rating system for SMEs using fuzzy-BWM and fuzzy-TOPSIS-Sort-C," Annals of Operations Research, Springer, vol. 325(2), pages 1197-1229, June.
    11. Diana Barro & Marco Corazza & Gianni Filograsso, 2023. "A ESG rating model for European SMEs using multi-criteria decision aiding," Working Papers 2023: 27, Department of Economics, University of Venice "Ca' Foscari".
    12. Pereira, André Alves & Pereira, Miguel Alves, 2023. "Energy storage strategy analysis based on the Choquet multi-criteria preference aggregation model: The Portuguese case," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    13. Zhen Zhang & Zhuolin Li, 2023. "Consensus-based TOPSIS-Sort-B for multi-criteria sorting in the context of group decision-making," Annals of Operations Research, Springer, vol. 325(2), pages 911-938, June.
    14. Erick P. Massami & Malima M. Manyasi, 2021. "Analysis of determinants of work performance for seafarers based on fuzzy Electre model," Journal of Shipping and Trade, Springer, vol. 6(1), pages 1-20, December.
    15. Liu, Xianliang & Ma, Yonghao, 2021. "A method to analyze the rank reversal problem in the ELECTRE II method," Omega, Elsevier, vol. 102(C).
    16. Paulo Cesar Schotten & Leydiana Sousa Pereira & Danielle Costa Morais, 2022. "Credit granting sorting model for financial organizations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-24, December.
    17. Kadziński, Miłosz & Stamenković, Mladen & Uniejewski, Maciej, 2022. "Stepwise benchmarking for multiple criteria sorting," Omega, Elsevier, vol. 108(C).
    18. Alvarez, Pavel Anselmo & Valdez, Cuitláhuac & Dutta, Bapi, 2022. "Analysis of the innovation capacity of Mexican regions with the multiple criteria hierarchy process," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    19. Pranith Kumar Roy & Krishnendu Shaw, 2022. "Developing a multi-criteria sustainable credit score system using fuzzy BWM and fuzzy TOPSIS," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(4), pages 5368-5399, April.
    20. Pereira, Miguel Alves & Marques, Rui Cunha, 2022. "Is sunshine regulation the new prescription to brighten up public hospitals in Portugal?," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).

    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:gam:jmathe:v:8:y:2020:i:11:p:1873-:d:436577. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.