Methodology and problems of expert assessment. Part 1. Ways to increase internal consistency of pairwise comparison matrix

The various fields of application of expert assessment methods for solving multicriteria selection problems are listed. A brief systematic analysis of a number of key methodological problems of the expert approach is performed, and general ways to overcome them are considered. A formal setting of the problem of increasing the internal consistency of the matrix of paired comparisons, reflecting the expert's opinion, is presented. Two different ways of solving the problem are proposed. The first method consists in constructing a graph reflecting the order of preference of the alternatives, followed by calculating the weights of the arcs and converting the elements of the matrix of paired comparisons so that the resulting matrix exceeds the initial one in terms of internal consistency. The second method is to generate an ideal matrix of paired comparisons based on a row or column of the original matrix, followed by a comparison of both matrices with each other. Both methods of adjusting the initial matrix of paired comparisons in order to increase internal consistency do not require additional information to perform it.

Authors: E. A. Burkov, P. I. Paderno, V. V. Rozen, E. A. Tolkacheva, D. A. Cherkasova

Direction: Informatics, Computer Technologies And Control

Keywords: internal consistency, preference graph, ideal matrix, pairwise comparison matrix, аnalytical hierarchy process, spanning tree, expert assessments

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