**6. Conclusions**

The stability of multicriteria MCDM methods is associated with the incomplete certainty of the data used for calculations.

This uncertainty is particularly evident when calculating the subjective weights of criteria based on expert assessments. Unstable estimates (ranking) in MCDM methods reduce the quality of the estimates and the reliability of the decision. The instability of the MCDM methods can result in an incorrect ranking of the evaluated alternatives, not the proper choice of the best option, inaccurate estimates of the criteria' significance, and the criteria weights' values in a particular situation and environment. Therefore, the problem investigated in this publication is relevant. The calculations show that the AHP method, as a mathematical method, is stable with respect to minor fluctuations in the elements of the comparison matrix. The transition from the Saaty scale integers 1-3-5-7-9 to close real numbers slightly changes the values of the weights. The relative error of the weight estimates that were insignificant varied between *δ* = 0.0531 (at 5% deviation) and *δ* = 0.116 (at 10% deviation).

The maximum relative error of the AHP method, related to the assessments of the experts themselves, the logic of their thinking, and psychology, is significantly greater than the error of AHP as a mathematical method. At the same time, changing the elements of the comparison matrix by units significantly affects the values of the eigenvector components of the matrix. The relative error of the estimates of the weights much higher and varied in the range *δ* = 0.5121 to *δ* = 0.7739.

The stability of the weights of the FAHP method is related not only to the factors listed above for the AHP method, but also to the use of Chang's algorithm for estimating weights. The calculations show that the algorithm itself is not universal, is not applicable for all matrices, and depends on the scale used for the estimates of the triangular numbers. If the evaluation scale is incorrectly selected, the weights may be zero for some matrices. The relative error of the FAHP method is significantly higher than that for the AHP method and varied from *δ* = 0.2421 to *δ* = 0.9797. It was anomalous (*δ* = 4.6606) in the case of a very small weight for a criterion.

The proposed asymmetric FAHP scale significantly improved the results: it eliminated the appearance of zero weights for criteria, reduced the values of the maximum relative errors, and showed a high degree of correlation with the weights obtained by the AHP method.

Regarding the novelty and relevance of this paper, we can point to the study of the stability of the AHP method, which depends on the instability of the estimates of the experts themselves, and the analysis of the stability of the FAHP method, which was clearly insufficiently studied earlier. This paper can be used to analyze the stability of specific MCDM methods by ranking the alternatives.

**Author Contributions:** V.P., E.K.Z. and I.V.-Z. conceived the presented idea. V.P. and I.V.-Z. developed the theory. I.V.-Z. performed the computations. E.K.Z. supervised the findings of this paper. All authors discussed the results and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
