A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method
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 a...
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| Format: | Article |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/554 |
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| author | Jiří Mazurek Radomír Perzina Jaroslav Ramík David Bartl |
| author_facet | Jiří Mazurek Radomír Perzina Jaroslav Ramík David Bartl |
| author_sort | Jiří Mazurek |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T05:16:24Z |
| format | Article |
| id | doaj.art-d33656b8371d4e519e4089b036356ab8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:16:24Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d33656b8371d4e519e4089b036356ab82023-12-03T12:45:48ZengMDPI AGMathematics2227-73902021-03-019555410.3390/math9050554A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst MethodJiří Mazurek0Radomír Perzina1Jaroslav Ramík2David Bartl3Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech RepublicDepartment of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech RepublicDepartment of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech RepublicDepartment of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava, Univerzitní Náměstí 1934/3, 733 40 Karviná, Czech RepublicIn 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.https://www.mdpi.com/2227-7390/9/5/554Best–Worst MethodEigenvalue MethodGeometric Mean MethodMonte Carlo simulationspairwise comparisonssensitivity |
| spellingShingle | Jiří Mazurek Radomír Perzina Jaroslav Ramík David Bartl A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method Mathematics Best–Worst Method Eigenvalue Method Geometric Mean Method Monte Carlo simulations pairwise comparisons sensitivity |
| title | A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method |
| title_full | A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method |
| title_fullStr | A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method |
| title_full_unstemmed | A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method |
| title_short | A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method |
| title_sort | numerical comparison of the sensitivity of the geometric mean method eigenvalue method and best worst method |
| topic | Best–Worst Method Eigenvalue Method Geometric Mean Method Monte Carlo simulations pairwise comparisons sensitivity |
| url | https://www.mdpi.com/2227-7390/9/5/554 |
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