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

Jiri Mazurek, Radomír Perzina, Jaroslav Ramík and David Bartl
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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

Mathematics, 2021, vol. 9, issue 5, 1-13

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.

Keywords: Best–Worst Method; Eigenvalue Method; Geometric Mean Method; Monte Carlo simulations; pairwise comparisons; sensitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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