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@article{55145,
author = {Mazurek, Jiří and Perzina, Radomír and Ramík, Jaroslav and Bartl, David},
article_number = {5},
doi = {http://dx.doi.org/10.3390/MATH9050554},
keywords = {Best–Worst Method; Eigenvalue Method; Geometric Mean Method; Monte Carlo simulations; pairwise comparisons; sensitivity},
language = {eng},
issn = {2227-7390},
journal = {Mathematics},
title = {A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method},
url = {https://www.mdpi.com/2227-7390/9/5/554},
volume = {9},
year = {2021}
}
TY - JOUR
ID - 55145
AU - Mazurek, Jiří - Perzina, Radomír - Ramík, Jaroslav - Bartl, David
PY - 2021
TI - A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method
JF - Mathematics
VL - 9
IS - 5
SP - 1-13
EP - 1-13
PB - MDPI
SN - 22277390
KW - Best–Worst Method
KW - Eigenvalue Method
KW - Geometric Mean Method
KW - Monte Carlo simulations
KW - pairwise comparisons
KW - sensitivity
UR - https://www.mdpi.com/2227-7390/9/5/554
N2 - 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.
ER -
MAZUREK, Jiří, Radomír PERZINA, Jaroslav RAMÍK a David BARTL. A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method. \textit{Mathematics}. MDPI, roč.~9, č.~5, s.~1-13. ISSN~2227-7390. doi:10.3390/MATH9050554. 2021.
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