IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v211y2013i1p493-50910.1007-s10479-013-1329-0.html
   My bibliography  Save this article

Inconsistency indices for pairwise comparison matrices: a numerical study

Author

Listed:
  • Matteo Brunelli
  • Luisa Canal
  • Michele Fedrizzi

Abstract

Evaluating the level of inconsistency of pairwise comparisons is often a crucial step in multi criteria decision analysis. Several inconsistency indices have been proposed in the literature to estimate the deviation of expert’s judgments from a situation of full consistency. This paper surveys and analyzes ten indices from the numerical point of view. Specifically, we investigate degrees of agreement between them to check how similar they are. Results show a wide range of behaviors, ranging from very strong to very weak degrees of agreement. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:493-509:10.1007/s10479-013-1329-0
    DOI: 10.1007/s10479-013-1329-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1329-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-013-1329-0?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. Michele Fedrizzi & Matteo Brunelli, 2009. "Fair Consistency Evaluation For Reciprocal Relations And In Group Decision Making," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 407-420.
    2. Marcin Anholcer & Volodymyr Babiy & Sándor Bozóki & Waldemar Koczkodaj, 2011. "A simplified implementation of the least squares solution for pairwise comparisons matrices," 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(4), pages 439-444, December.
    3. Linares, Pedro, 2009. "Are inconsistent decisions better? An experiment with pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 193(2), pages 492-498, March.
    4. Saaty, Thomas L., 1994. "Highlights and critical points in the theory and application of the Analytic Hierarchy Process," European Journal of Operational Research, Elsevier, vol. 74(3), pages 426-447, May.
    5. Osei-Bryson, Kweku-Muata, 2006. "An action learning approach for assessing the consistency of pairwise comparison data," European Journal of Operational Research, Elsevier, vol. 174(1), pages 234-244, October.
    6. Stein, William E. & Mizzi, Philip J., 2007. "The harmonic consistency index for the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 177(1), pages 488-497, February.
    7. Salo, Ahti A. & Hamalainen, Raimo P., 1995. "Preference programming through approximate ratio comparisons," European Journal of Operational Research, Elsevier, vol. 82(3), pages 458-475, May.
    8. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    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. Pedro Linares & Sara Lumbreras & Alberto Santamaría & Andrea Veiga, 2016. "How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP," Annals of Operations Research, Springer, vol. 245(1), pages 227-244, October.
    2. Yuji Sato & Kim Hua Tan, 2023. "Inconsistency indices in pairwise comparisons: an improvement of the Consistency Index," Annals of Operations Research, Springer, vol. 326(2), pages 809-830, July.
    3. Banai, Reza, 2010. "Evaluation of land use-transportation systems with the Analytic Network Process," The Journal of Transport and Land Use, Center for Transportation Studies, University of Minnesota, vol. 3(1), pages 85-112.
    4. Valentin Bertsch & Wolf Fichtner, 2016. "A participatory multi-criteria approach for power generation and transmission planning," Annals of Operations Research, Springer, vol. 245(1), pages 177-207, October.
    5. Liu Fang & Peng Yanan & Zhang Weiguo & Pedrycz Witold, 2017. "On Consistency in AHP and Fuzzy AHP," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 128-147, April.
    6. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    7. József Temesi, 2011. "Pairwise comparison matrices and the error-free property of the decision maker," 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 239-249, June.
    8. Jiménez, Antonio & Mateos, Alfonso & Sabio, Pilar, 2013. "Dominance intensity measure within fuzzy weight oriented MAUT: An application," Omega, Elsevier, vol. 41(2), pages 397-405.
    9. Abrahamsen, Eirik Bjorheim & Milazzo, Maria Francesca & Selvik, Jon T. & Asche, Frank & Abrahamsen, HÃ¥kon Bjorheim, 2020. "Prioritising investments in safety measures in the chemical industry by using the Analytic Hierarchy Process," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    10. Phillips, Jason, 2013. "Determining the sustainability of large-scale photovoltaic solar power plants," Renewable and Sustainable Energy Reviews, Elsevier, vol. 27(C), pages 435-444.
    11. Guo, Min & Yang, Jian-Bo & Chin, Kwai-Sang & Wang, Hongwei, 2007. "Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1294-1312, November.
    12. 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.
    13. Elena Carrara & Rebecca Ciavarella & Stefania Boglietti & Martina Carra & Giulio Maternini & Benedetto Barabino, 2021. "Identifying and Selecting Key Sustainable Parameters for the Monitoring of e-Powered Micro Personal Mobility Vehicles. Evidence from Italy," Sustainability, MDPI, vol. 13(16), pages 1-22, August.
    14. Dinulescu Ruxandra & Dobrin Cosmin, 2022. "Applying the fuzzy analytical hierarchy process for classifying and prioritizing healthcare quality attributes," Management & Marketing, Sciendo, vol. 17(1), pages 15-40, March.
    15. Helena Gaspars-Wieloch, 2024. "AHP based on scenarios and the optimism coefficient for new and risky projects: case of independent criteria," Annals of Operations Research, Springer, vol. 341(2), pages 937-961, October.
    16. Ian Durbach, 2019. "Scenario planning in the analytic hierarchy process," Futures & Foresight Science, John Wiley & Sons, vol. 1(2), June.
    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. Tung, S. L. & Tang, S. L., 1998. "A comparison of the Saaty's AHP and modified AHP for right and left eigenvector inconsistency," European Journal of Operational Research, Elsevier, vol. 106(1), pages 123-128, April.
    19. Liang, Liang & Wang, Guohua & Hua, Zhongsheng & Zhang, Bin, 2008. "Mapping verbal responses to numerical scales in the analytic hierarchy process," Socio-Economic Planning Sciences, Elsevier, vol. 42(1), pages 46-55, March.
    20. Chin-Yi Chen & Jih-Jeng Huang, 2022. "Deriving Fuzzy Weights from the Consistent Fuzzy Analytic Hierarchy Process," Mathematics, MDPI, vol. 10(19), pages 1-12, September.

    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:211:y:2013:i:1:p:493-509:10.1007/s10479-013-1329-0. 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.