IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v64y2006i2p271-284.html
   My bibliography  Save this article

Inferring Efficient Weights from Pairwise Comparison Matrices

Author

Listed:
  • R. Blanquero
  • E. Carrizosa
  • E. Conde

Abstract

Several multi-criteria-decision-making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance.One of the most popular ways to infer such weights is the analytic hierarchy process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the eigenvector method or the least (logarithmic) squares. Since different procedures yield different results (weights) we pose the problem of describing the set of weights obtained by “sensible” methods: those which are efficient for the (vector-) optimization problem of simultaneous minimization of discrepancies. A characterization of the set of efficient solutions is given, which enables us to assert that the least-logarithmic-squares solution is always efficient, whereas the (widely used) eigenvector solution is not, in some cases, efficient, thus its use in practice may be questionable. Copyright Springer-Verlag 2006

Suggested Citation

  • R. Blanquero & E. Carrizosa & E. Conde, 2006. "Inferring Efficient Weights from Pairwise Comparison Matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 271-284, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:271-284
    DOI: 10.1007/s00186-006-0077-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0077-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-006-0077-1?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. Lootsma, F. A., 1996. "A model for the relative importance of the criteria in the Multiplicative AHP and SMART," European Journal of Operational Research, Elsevier, vol. 94(3), pages 467-476, November.
    2. Saaty, Thomas L., 1990. "Eigenvector and logarithmic least squares," European Journal of Operational Research, Elsevier, vol. 48(1), pages 156-160, September.
    3. Cook, Wade D. & Kress, Moshe, 1988. "Deriving weights from pairwise comparison ratio matrices: An axiomatic approach," European Journal of Operational Research, Elsevier, vol. 37(3), pages 355-362, December.
    4. Thomas L. Saaty, 1994. "How to Make a Decision: The Analytic Hierarchy Process," Interfaces, INFORMS, vol. 24(6), pages 19-43, December.
    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. Csató, László, 2024. "Right-left asymmetry of the eigenvector method: A simulation study," European Journal of Operational Research, Elsevier, vol. 313(2), pages 708-717.
    2. Fernandes, Rosário & Furtado, Susana, 2022. "Efficiency of the principal eigenvector of some triple perturbed consistent matrices," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1007-1015.
    3. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    4. Judit Oláh & József Popp & Szabolcs Duleba & Anna Kiss & Zoltán Lakner, 2021. "Positioning Bio-Based Energy Systems in a Hypercomplex Decision Space—A Case Study," Energies, MDPI, vol. 14(14), pages 1-23, July.
    5. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    6. Carrizosa, Emilio, 2012. "On approximate Monetary Unit Sampling," European Journal of Operational Research, Elsevier, vol. 217(2), pages 479-482.
    7. Jana Siebert, 2019. "Fuzzy eigenvector method for deriving normalized fuzzy priorities from fuzzy multiplicative pairwise comparison matrices," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 175-197, June.
    8. Szádoczki, Zsombor & Bozóki, Sándor & Tekile, Hailemariam Abebe, 2022. "Filling in pattern designs for incomplete pairwise comparison matrices: (Quasi-)regular graphs with minimal diameter," Omega, Elsevier, vol. 107(C).
    9. Conde, Eduardo & de la Paz Rivera Pérez, María, 2010. "A linear optimization problem to derive relative weights using an interval judgement matrix," European Journal of Operational Research, Elsevier, vol. 201(2), pages 537-544, March.
    10. Miguel Hervás-Peralta & Sara Poveda-Reyes & Gemma Dolores Molero & Francisco Enrique Santarremigia & Juan-Pascual Pastor-Ferrando, 2019. "Improving the Performance of Dry and Maritime Ports by Increasing Knowledge about the Most Relevant Functionalities of the Terminal Operating System (TOS)," Sustainability, MDPI, vol. 11(6), pages 1-23, March.
    11. Marcin Anholcer & János Fülöp, 2019. "Deriving priorities from inconsistent PCM using network algorithms," Annals of Operations Research, Springer, vol. 274(1), pages 57-74, March.
    12. Mariia Dushenko & Clemet Thærie Bjorbæk & Kenn Steger-Jensen, 2018. "Application of a Sustainability Model for Assessing the Relocation of a Container Terminal: A Case Study of Kristiansand Port," Sustainability, MDPI, vol. 11(1), pages 1-18, December.
    13. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.
    14. Bozóki, Sándor & Fülöp, János, 2018. "Efficient weight vectors from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 264(2), pages 419-427.

    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. Conde, Eduardo & de la Paz Rivera Pérez, María, 2010. "A linear optimization problem to derive relative weights using an interval judgement matrix," European Journal of Operational Research, Elsevier, vol. 201(2), pages 537-544, March.
    2. Hartvigsen, David, 2005. "Representing the strengths and directions of pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 163(2), pages 357-369, June.
    3. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    4. Tofallis, Chris, 2020. "Which formula for national happiness?," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    5. Concepcion Roman & Juan Carlos Martin & Raquel Espino, 2011. "Using Stated Preferences (Sp) To Analyze The Service Quality Of Public Transport," ERSA conference papers ersa11p86, European Regional Science Association.
    6. Bhatta, Arun & Bigsby, Hugh R. & Cullen, Ross, 2011. "Alternative to Comprehensive Ecosystem Services Markets: The Contribution of Forest-Related Programs in New Zealand," 2011 Conference, August 25-26, 2011, Nelson, New Zealand 115350, New Zealand Agricultural and Resource Economics Society.
    7. Daniel Schatz & Rabih Bashroush, 0. "Economic valuation for information security investment: a systematic literature review," Information Systems Frontiers, Springer, vol. 0, pages 1-24.
    8. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    9. Chandratilake, S.R. & Dias, W.P.S., 2013. "Sustainability rating systems for buildings: Comparisons and correlations," Energy, Elsevier, vol. 59(C), pages 22-28.
    10. Certa, Antonella & Hopps, Fabrizio & Inghilleri, Roberta & La Fata, Concetta Manuela, 2017. "A Dempster-Shafer Theory-based approach to the Failure Mode, Effects and Criticality Analysis (FMECA) under epistemic uncertainty: application to the propulsion system of a fishing vessel," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 69-79.
    11. Bertomeu, M. & Romero, C., 2001. "Managing forest biodiversity: a zero-one goal programming approach," Agricultural Systems, Elsevier, vol. 68(3), pages 197-213, June.
    12. Hyunjin Lim & Sunkuk Kim & Yonggu Kim & Seunghyun Son, 2021. "Relative Importance Analysis of Safety Climate Evaluation Factors Using Analytical Hierarchical Process (AHP)," Sustainability, MDPI, vol. 13(8), pages 1-14, April.
    13. Ormerod, R.J., 2014. "Critical rationalism in practice: Strategies to manage subjectivity in OR investigations," European Journal of Operational Research, Elsevier, vol. 235(3), pages 784-797.
    14. Carayannis, Elias G. & Goletsis, Yorgos & Grigoroudis, Evangelos, 2018. "Composite innovation metrics: MCDA and the Quadruple Innovation Helix framework," Technological Forecasting and Social Change, Elsevier, vol. 131(C), pages 4-17.
    15. Sunita Guru & Jitendra Nenavani & Vipul Patel & Nityesh Bhatt, 2020. "Ranking of perceived risks in online shopping," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 47(2), pages 137-152, June.
    16. Rimvydas Labanauskis & Aurelija Kasparavičiūtė & Vida Davidavičienė & Dovilė Deltuvienė, 2018. "Towards quality assurance of the study process using the Multi-Criteria Decision-Making Method," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 6(2), pages 799-819, December.
    17. Yusuf Ersoy & Ali Tehci, 2023. "Relationship marketing orientation in healthcare organisations with the AHP method," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(1), pages 35-45.
    18. Bojan Srdjevic & Yvonilde Medeiros, 2008. "Fuzzy AHP Assessment of Water Management Plans," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(7), pages 877-894, July.
    19. Ali Yalcin & Fikri Bulut, 2007. "Landslide susceptibility mapping using GIS and digital photogrammetric techniques: a case study from Ardesen (NE-Turkey)," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 41(1), pages 201-226, April.
    20. 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.

    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:mathme:v:64:y:2006:i:2:p:271-284. 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.