Method for Evaluating Inhomogeneous Alternatives with the Hierarchical Structure of Unrelated Criteria Based on Medium-Consistent Matrix of Pair Comparisons

Abstract

This article discusses inhomogeneous alternatives with unrelated criteria with a cluster-hierarchical structure. The heterogeneity of alternatives is characterized by differences in the structure and number of criteria used in the process of obtaining an integral indicator. In order to construct an integral indicator, we form a block matrix of pairwise comparisons, the elements of which are taken from separate matrices of pairwise comparisons obtained by experts in the course of previous studies. In order to construct the missing elements of the block matrix, we formulate a rule describing the construction of medium-matched matrices of pairwise comparisons due to which the missing elements of the block matrix are calculated without the involvement of experts. This method allows to construct more than 60% of elements of the new block matrix, and takes into account the inconsistency in the paired comparisons made by experts. Also, this method allows to calculate the weight coefficients for a generalized integral indicator formed from individual elements of the matrix of pairwise comparisons obtained during the previous study, which saves costs arising during preliminary examination. In order to solve this problem, we use a cluster-hierarchical approach, as well as methods of decomposition and synthesis. The results of the paper can be applied in problems of the theory of decision making, in the class of problems of integral estimation of multicriteria objects, and in problems with weak formalization.