IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v253y2015icp387-394.html

Pairwise comparisons simplified

Author

Listed:
  • Koczkodaj, W.W.
  • Szybowski, J.

Abstract

This study examines the notion of generators of a pairwise comparisons matrix. Such approach decreases the number of pairwise comparisons from n·(n-1) to n-1. An algorithm of reconstructing of the PC matrix from its set of generators is presented.

Suggested Citation

  • Koczkodaj, W.W. & Szybowski, J., 2015. "Pairwise comparisons simplified," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 387-394.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:387-394
    DOI: 10.1016/j.amc.2014.12.069
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314017238
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.12.069?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. K K F Yuen, 2012. "Pairwise opposite matrix and its cognitive prioritization operators: comparisons with pairwise reciprocal matrix and analytic prioritization operators," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 322-338, March.
    3. 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.
    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. Szybowski, Jacek & Kułakowski, Konrad & Prusak, Anna, 2020. "New inconsistency indicators for incomplete pairwise comparisons matrices," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 138-145.
    2. Irina Vinogradova-Zinkevič, 2023. "Comparative Sensitivity Analysis of Some Fuzzy AHP Methods," Mathematics, MDPI, vol. 11(24), pages 1-41, December.
    3. Benítez, Julio & Koczkodaj, Waldemar W. & Kowalczyk, Adam, 2024. "Computationally efficient orthogonalization for pairwise comparisons method," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    4. 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.
    5. Hassan, Shamsu & Wang, Jin & Kontovas, Christos & Bashir, Musa, 2022. "An assessment of causes and failure likelihood of cross-country pipelines under uncertainty using bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    6. Hristos Karahalios, 2017. "Evaluating the knowledge of experts in the maritime regulatory field," Maritime Policy & Management, Taylor & Francis Journals, vol. 44(4), pages 426-441, May.
    7. Jacek Szybowski & Konrad Kułakowski & Sebastian Ernst, 2024. "Almost optimal manipulation of pairwise comparisons of alternatives," Journal of Global Optimization, Springer, vol. 90(1), pages 243-259, September.

    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 & Michele Fedrizzi, 2019. "A general formulation for some inconsistency indices of pairwise comparisons," Annals of Operations Research, Springer, vol. 274(1), pages 155-169, March.
    2. Kułakowski, Konrad, 2018. "Inconsistency in the ordinal pairwise comparisons method with and without ties," European Journal of Operational Research, Elsevier, vol. 270(1), pages 314-327.
    3. 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.
    4. Li, Kevin W. & Wang, Zhou-Jing & Tong, Xiayu, 2016. "Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices," European Journal of Operational Research, Elsevier, vol. 250(2), pages 628-638.
    5. Wang, Zhou-Jing, 2015. "A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”," European Journal of Operational Research, Elsevier, vol. 247(3), pages 867-871.
    6. Chih-Hsuan Wang, 2019. "Association rule mining and cognitive pairwise rating based portfolio analysis for product family design," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1911-1922, April.
    7. Lundy, Michele & Siraj, Sajid & Greco, Salvatore, 2017. "The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis," European Journal of Operational Research, Elsevier, vol. 257(1), pages 197-208.
    8. 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.
    9. Zhou, Wei & Xu, Zeshui, 2016. "Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites," European Journal of Operational Research, Elsevier, vol. 254(2), pages 610-621.
    10. Sangeeta Pant & Anuj Kumar & Mangey Ram & Yury Klochkov & Hitesh Kumar Sharma, 2022. "Consistency Indices in Analytic Hierarchy Process: A Review," Mathematics, MDPI, vol. 10(8), pages 1-15, April.
    11. Kevin Kam Fung Yuen, 2022. "Decision models for information systems planning using primitive cognitive network process: comparisons with analytic hierarchy process," Operational Research, Springer, vol. 22(3), pages 1759-1785, July.
    12. 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.
    13. 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.
    14. Xiaobo Zhang & Chengshan Wang & Jie Fan & Huijun Wang & Hailong Li, 2020. "Optimizing the Analytic Hierarchy Process through a Suitability Evaluation of Underground Space Development in Tonghu District, Huizhou City," Energies, MDPI, vol. 13(3), pages 1-22, February.
    15. 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.
    16. Jiří Mazurek & Konrad Kulakowski, 2020. "Information gap in value propositions of business models of language schools," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 77-89.
    17. Kułakowski, Konrad, 2015. "Notes on order preservation and consistency in AHP," European Journal of Operational Research, Elsevier, vol. 245(1), pages 333-337.
    18. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    19. Zsombor Szádoczki & Sándor Bozóki & Patrik Juhász & Sergii V. Kadenko & Vitaliy Tsyganok, 2023. "Incomplete pairwise comparison matrices based on graphs with average degree approximately 3," Annals of Operations Research, Springer, vol. 326(2), pages 783-807, July.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:apmaco:v:253:y:2015:i:c:p:387-394. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.