The Approximation Matrix Method and its Comparison with the Analytical Hierarchy Process by T. Saaty

Abstract

The article presents an optimization method for the formation of quantitative weights of objects (importance of criteria, priorities of alternatives) according to the initial expert judgment matrix in multi-criteria selection problems. Since the matrix of pairwise comparisons can be considered as some perturbation of the multiplicative matrix, the proposed method is based on the approximation of the original matrix of pairwise comparisons by the multiplicative matrix according to the matrix criterion of minimum distances between matrices. There is a one-to-one mapping between the elements of the weight vectors and the elements of the multiplicative matrix. For the first time, using a specific example using the matrix criterion, a relative estimate of the approximate solution of the Analytical Hierarchy Process by T. Saaty concerning the optimal solution obtained by the approximation matrix method is given. On account of the approximation matrix method being mathematically justified and due to the simplicity of finding optimal solutions, it can be recommended instead of the Analytical Hierarchy Process by T. Saaty.