Refinement of non-linear quantitative estimates of the Saati scale advantages indicators

Анотація

Any effective management is accompanied by a solution multi-criteria decision-making problem (MCDMP). Among the relevant methods and technologies, the Analytic Hierarchy Process has been the leading efficiency for several decades (AHP), developed by T. L. Saaty. The implementation of AHP consists in determining local vectors of priorities — normalized weight coefficients (NWC) — at all levels of the hierarchy of the MCDMP being solved. Their further synthesis leads to a global vector — integrative assessments of the studied alternatives, which and only which have the systemic property of emergence, which facilitates a thorough choice of the best of them. Despite the positive results of numerous studies on the application and improvement of AHP, the need to construct a pairwise comparison matrix (PCM) remains unchanged, the solution of which actually leads to obtaining the desired priorities-NWC. The specified PCM is built based on direct and inverse linear score estimates-quantitative equivalents of linguistic inducers of preference (IP). Which is actually an artificial replacement of measurements in the scoring ranking scale with measurements in the interval scale. Therefore, the corresponding solutions are not optimal, because linearity is not a property of human thinking and orientation on it can lead to erroneous results. The ranking of linguistic IRs of the Saaty scale is obvious, therefore, using the mathematical method of prioritization (MoP), known in systems analysis as the “leader problem”, nonlinear NWCs of all nine IPs, measured already in an absolute scale unique in qualimetric properties, were obtained. The acceptability for research of the results of the second iteration of the MoP is justified. The analytical description of the indicated nonlinearity was carried out in a step scale. It was established that the nonlinearity itself increased the sensitivity of the scale to the measurement of priority by 16.5 times. Quantitative estimates of the ratio of linguistic IPs associated with the modifier “very” improved in relation to the indicators of the linear scale: by 20 % for the ratio IP7–IP6, and by 17 % and 39 % for the ratio IP8–IP7 and IP8–IP6, respectively. This indicates a greater harmonization of the quantitative and qualitative adequacy of the Saaty’s scale.

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