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.
Highlights
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
The Geometric Mean Method (GMM) proposed by Crawford [11] and the Eigenvalue Method (EVM) proposed by Saaty [7] are the most popular methods for deriving weights from pairwise comparisons arranged in the form of a pairwise comparison (PC) matrix
Since the Best–Worst Method (BWM) is “handicapped” by the lower number of pairwise comparisons required, we performed Welch’s test for sensitivity equality of all three methods, where the sensitivity of the BWM was adjusted by the factor n(n2n−−1)3/2, corresponding to the number of pairwise comparisons required by the BWM and EVM/GMM, respectively; see Figure 3
Summary
The values of cij and c ji indicate the relative importance (or preference) of the objects i and j. In the context of the BWM, the compared objects are criteria. The set of n criteria to be compared and ranked is denoted as F = { F1 , . The matrix C = [cij ] is said to be reciprocal if ∀i, j ∈ {1, . C = [cij ] is said to be consistent if ∀i, j, k ∈ {1, . Note that if C = [cij ] is consistent, it is reciprocal, but not vice versa. It is assumed that a PC matrix is always reciprocal. The reciprocity condition seems to be natural in many decision-making situations.
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