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Article

On the Geometric Mean Method for Incomplete Pairwise Comparisons

Department of Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland
Mathematics 2020, 8(11), 1873; https://doi.org/10.3390/math8111873
Received: 30 September 2020 / Revised: 16 October 2020 / Accepted: 16 October 2020 / Published: 29 October 2020
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step. View Full-Text
Keywords: pairwise comparisons; geometric mean method; incompleteness; incomplete pairwise comparison matrices pairwise comparisons; geometric mean method; incompleteness; incomplete pairwise comparison matrices
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MDPI and ACS Style

Kułakowski, K. On the Geometric Mean Method for Incomplete Pairwise Comparisons. Mathematics 2020, 8, 1873. https://doi.org/10.3390/math8111873

AMA Style

Kułakowski K. On the Geometric Mean Method for Incomplete Pairwise Comparisons. Mathematics. 2020; 8(11):1873. https://doi.org/10.3390/math8111873

Chicago/Turabian Style

Kułakowski, Konrad. 2020. "On the Geometric Mean Method for Incomplete Pairwise Comparisons" Mathematics 8, no. 11: 1873. https://doi.org/10.3390/math8111873

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