Transformation of numerical scales for pairwise comparisons: AHP, Dematel, BWM, SWARA

The paper presents an overview and comparative analysis of four weighting methods for multi-criteria decision-making problem based on pairwise comparisons: AHP, Dematel, BWM and SWARA. It is demonstrate, by examples that the reliability of evaluations largely depends on the correct use of the pairwise comparison tool: evaluations are given on a verbal scale, then converted into quantitative values and then the criteria priorities are calculated. All stages of pairwise comparisons are multivariate. In particular, the validity of this decision-making tool depends on the choice of numerical scale and the method of prioritization. Given the importance, a set of concepts relating to linguistic variables, linguistic pairwise comparison matrices, and numerical scale (scale function) are presented in detail. It is demonstrate that the information of the pairwise comparison matrix in AHP is higher and is sufficient for the unambiguous implementation of the Dematel, BWM and SWARA methods. Although the reliability of the solution for a larger number of input information is considered higher, nevertheless, it cannot be argued that the decision of the AHP are more significant. The emphasis in this study is on the transformation of the numerical scale. The transformation of the numerical scale a directly related to the mental representation of the verbal scale, since the decision maker forms the scale according to his mental representation. It is demonstrate that the compression of the numerical scale leads to the alignment of priorities. The trend is the same for all types of numerical scales and prioritization methods, but the process occurs at different speeds. For scales with a smaller number of gradations, a decrease in the degree of priority on the numerical scale is characteristic, which leads to a decrease in the difference in weights. In particular, this difference can be adjusted by scaling.