IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i3p604-d1046116.html
   My bibliography  Save this article

When Fairness Meets Consistency in AHP Pairwise Comparisons

Author

Listed:
  • Zorica Dodevska

    (The Institute for Artificial Intelligence Research and Development of Serbia, 1 Fruškogorska, 21000 Novi Sad, Serbia)

  • Sandro Radovanović

    (Faculty of Organizational Sciences, The University of Belgrade, 154 Jove Ilića, 11000 Belgrade, Serbia
    These authors contributed to this work according to the reported order.)

  • Andrija Petrović

    (Faculty of Organizational Sciences, The University of Belgrade, 154 Jove Ilića, 11000 Belgrade, Serbia
    These authors contributed to this work according to the reported order.)

  • Boris Delibašić

    (Faculty of Organizational Sciences, The University of Belgrade, 154 Jove Ilića, 11000 Belgrade, Serbia
    These authors contributed to this work according to the reported order.)

Abstract

We propose introducing fairness constraints to one of the most famous multi-criteria decision-making methods, the analytic hierarchy process (AHP). We offer a solution that guarantees consistency while respecting legally binding fairness constraints in AHP pairwise comparison matrices. Through a synthetic experiment, we generate the comparison matrices of different sizes and ranges/levels of the initial parameters (i.e., consistency ratio and disparate impact). We optimize disparate impact for various combinations of these initial parameters and observed matrix sizes while respecting an acceptable level of consistency and minimizing deviations of pairwise comparison matrices (or their upper triangles) before and after the optimization. We use a metaheuristic genetic algorithm to set the dually motivating problem and operate a discrete optimization procedure (in connection with Saaty’s 9-point scale). The results confirm the initial hypothesis (with 99.5% validity concerning 2800 optimization runs) that achieving fair ranking while respecting consistency in AHP pairwise comparison matrices (when comparing alternatives regarding given criterium) is possible, thus meeting two challenging goals simultaneously. This research contributes to the initiatives directed toward unbiased decision-making, either automated or algorithm-assisted (which is the case covered by this research).

Suggested Citation

  • Zorica Dodevska & Sandro Radovanović & Andrija Petrović & Boris Delibašić, 2023. "When Fairness Meets Consistency in AHP Pairwise Comparisons," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:604-:d:1046116
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/3/604/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/3/604/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abbas Mardani & Edmundas Kazimieras Zavadskas & Kannan Govindan & Aslan Amat Senin & Ahmad Jusoh, 2016. "VIKOR Technique: A Systematic Review of the State of the Art Literature on Methodologies and Applications," Sustainability, MDPI, vol. 8(1), pages 1-38, January.
    2. Nolberto Munier & Eloy Hontoria, 2021. "Uses and Limitations of the AHP Method," Management for Professionals, Springer, number 978-3-030-60392-2, December.
    3. Chen, Chailin & Cook, Wade D. & Imanirad, Raha & Zhu, Joe, 2020. "Balancing Fairness and Efficiency: Performance Evaluation with Disadvantaged Units in Non-homogeneous Environments," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1003-1013.
    4. Sándor Bozóki & János Fülöp & Attila Poesz, 2015. "On reducing inconsistency of pairwise comparison matrices below an acceptance threshold," 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. 23(4), pages 849-866, December.
    5. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    6. Toly Chen, 2021. "A diversified AHP-tree approach for multiple-criteria supplier selection," Computational Management Science, Springer, vol. 18(4), pages 431-453, October.
    7. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Valdecy Pereira & Helder Costa, 2015. "Nonlinear programming applied to the reduction of inconsistency in the AHP method," Annals of Operations Research, Springer, vol. 229(1), pages 635-655, June.
    9. 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.
    10. Liberatore, Matthew J. & Nydick, Robert L., 2008. "The analytic hierarchy process in medical and health care decision making: A literature review," European Journal of Operational Research, Elsevier, vol. 189(1), pages 194-207, August.
    11. Serafim Opricovic, 2009. "A Compromise Solution in Water Resources Planning," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(8), pages 1549-1561, June.
    12. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    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. Liang, Fuqi & Brunelli, Matteo & Rezaei, Jafar, 2020. "Consistency issues in the best worst method: Measurements and thresholds," Omega, Elsevier, vol. 96(C).
    2. Wenshuai Wu & Gang Kou, 2016. "A group consensus model for evaluating real estate investment alternatives," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-10, December.
    3. Hanwen Chen & Wang Dong & Hongling Han & Nan Zhou, 2017. "A comprehensive and quantitative internal control index: construction, validation, and impact," Review of Quantitative Finance and Accounting, Springer, vol. 49(2), pages 337-377, August.
    4. Giacomo Falcone & Anna Irene De Luca & Teodora Stillitano & Alfio Strano & Giuseppa Romeo & Giovanni Gulisano, 2016. "Assessment of Environmental and Economic Impacts of Vine-Growing Combining Life Cycle Assessment, Life Cycle Costing and Multicriterial Analysis," Sustainability, MDPI, vol. 8(8), pages 1-34, August.
    5. Jean-Pierre Magnot & Jiří Mazurek & Viera Cernanova, 2021. "A gradient method for inconsistency reduction of pairwise comparisons matrices," Working Papers hal-03313878, HAL.
    6. Matthew Liberatore & Robert Nydick & Constantine Daskalakis & Elisabeth Kunkel & James Cocroft & Ronald Myers, 2009. "Helping Men Decide About Scheduling a Prostate Cancer Screening Exam," Interfaces, INFORMS, vol. 39(3), pages 209-217, June.
    7. Marcos Antonio Alves & Ivan Reinaldo Meneghini & António Gaspar-Cunha & Frederico Gadelha Guimarães, 2023. "Machine Learning-Driven Approach for Large Scale Decision Making with the Analytic Hierarchy Process," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    8. James G. Dolan & Emily Boohaker & Jeroan Allison & Thomas F. Imperiale, 2013. "Patients’ Preferences and Priorities Regarding Colorectal Cancer Screening," Medical Decision Making, , vol. 33(1), pages 59-70, January.
    9. Jana Krejčí & Alessio Ishizaka, 2018. "FAHPSort: A Fuzzy Extension of the AHPSort Method," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1119-1145, July.
    10. 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.
    11. Yousaf Ali & Zain Aslam & Hammad Sajid Dar & UbaidUllah Mumtaz, 2018. "A multi-criteria decision analysis of solid waste treatment options in Pakistan: Lahore City—a case in point," Environment Systems and Decisions, Springer, vol. 38(4), pages 528-543, December.
    12. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2023. "A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets," Mathematics, MDPI, vol. 11(2), pages 1-26, January.
    13. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    14. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    15. Li, Peiluan & Han, Liqin & Xu, Changjin & Peng, Xueqing & Rahman, Mati ur & Shi, Sairu, 2023. "Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    16. Abdelkader Moumen & Abdelaziz Mennouni, 2022. "A New Projection Method for a System of Fractional Cauchy Integro-Differential Equations via Vieta–Lucas Polynomials," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    17. Hanming Li & Xingquan Chen & Yiwei Fang, 2021. "The Development Strategy of Home-Based Exercise in China Based on the SWOT-AHP Model," IJERPH, MDPI, vol. 18(3), pages 1-12, January.
    18. Ana Mehak & Yongtong Mu & Muhammad Mohsin & Xing-Can Zhang, 2023. "MCDM-Based Ranking and Prioritization of Fisheries’ Risks: A Case Study of Sindh, Pakistan," Sustainability, MDPI, vol. 15(11), pages 1-21, May.
    19. Najariyan, Marzieh & Qiu, Li, 2023. "Singular fuzzy fractional quadratic regulator problem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    20. Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.

    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:11:y:2023:i:3:p:604-:d:1046116. 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.