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A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method

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  • Jiří Mazurek

    (Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech Republic)

  • Radomír Perzina

    (Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech Republic)

  • Jaroslav Ramík

    (Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech Republic)

  • David Bartl

    (Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech Republic)

Abstract

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

Suggested Citation

  • Jiří Mazurek & Radomír Perzina & Jaroslav Ramík & David Bartl, 2021. "A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:554-:d:511618
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    References listed on IDEAS

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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8.
    2. Murat Köksalan & Jyrki Wallenius & Stanley Zionts, 2011. "Multiple Criteria Decision Making:From Early History to the 21st Century," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8042, September.
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    Cited by:

    1. Frank Werner, 2021. "Special Issue “Mathematical Methods for Operations Research Problems”," Mathematics, MDPI, vol. 9(21), pages 1-4, October.
    2. Nikolai Krivulin & Alexey Prinkov & Igor Gladkikh, 2022. "Using Pairwise Comparisons to Determine Consumer Preferences in Hotel Selection," Mathematics, MDPI, vol. 10(5), pages 1-25, February.

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