Method of indirect preferences for forming criterion weights with a multi-level structure

The method of forming criterion weights in tasks of multi-criteria evaluation of objects with a multi-level structure of indicators presented in the form of a hierarchical tree, is shown. The weights values are calculated on the basis of indirect measurement of preferences of adjacent pairs of local weights of criteria included in the vertices of a higher level of the hierarchical tree, in the form of expert assessments in the quantitative scale of relations. The calculation of quantitative weights first comes down to lexicographic sorting by descending order of criteria importance at each level of the hierarchy that are included in the vertices of a higher level, as a result of which the number of expert comparisons of adjacent pairs in the scale of relations is reduced. The formation of local coefficients of the criteria importance is mathematically justified and is based on a matrix with special properties. A comparative analysis of the proposed method for forming quantitative weights with the method of hierarchy analysis, the least squares method and the approximation matrix method based on the matrix of paired comparisons, is given. An example is given of solving the problem of multi-criteria evaluation of combat aircraft that participated in the tender, according to the tactical and technical characteristics presented in various measurement scales.