MAZUREK, Jiří, Radomír PERZINA, Jaroslav RAMÍK and David BARTL. A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method. Mathematics. MDPI, vol. 9, No 5, p. 1-13. ISSN 2227-7390. doi:10.3390/MATH9050554. 2021.
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Basic information
Original name A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method
Authors MAZUREK, Jiří (203 Czech Republic, guarantor, belonging to the institution), Radomír PERZINA (203 Czech Republic, belonging to the institution), Jaroslav RAMÍK (203 Czech Republic, belonging to the institution) and David BARTL (203 Czech Republic, belonging to the institution).
Edition Mathematics, MDPI, 2021, 2227-7390.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10102 Applied mathematics
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19520/21:A0000189
Organization unit School of Business Administration in Karvina
Doi http://dx.doi.org/10.3390/MATH9050554
UT WoS 000628360000001
Keywords in English Best–Worst Method; Eigenvalue Method; Geometric Mean Method; Monte Carlo simulations; pairwise comparisons; sensitivity
Tags impakt
Tags International impact, Reviewed
Links GA21-03085S, research and development project.
Changed by Changed by: Miroslava Snopková, učo 43819. Changed: 12/4/2022 10:23.
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.
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