APPROXIMATION MATRIX METHOD FOR WEIGHTS FORMATION OF OBJECTS IN MULTICRITERIA PROBLEMS

Abstract

The article presents an optimization method for the formation of quantitative weights of objects (importance of criteria, priorities of alternatives) according to the original expert judgment matrix in multicriteria selection problems. Since the pairwise comparison matrix can be considered as some perturbation of the multiplicative matrix, the proposed method is based on the approximation of the original pairwise comparison matrix by a multiplicative matrix according to the matrix criterion of minimum distances between matrices. A comparative analysis of the effectiveness of the new method with the well-known method of the analytical hierarchy of T. Saaty is carried out according to the criterion of closeness to the original judgment matrix of multiplicative matrices, the elements of which are reconstructed from the found normalized elements of the weights of objects. On the example of solving the problem for weights forming of the importance of criteria, the accuracy of the approximate solution of the analytical hierarchy method is estimated. This method is mathematically substantiated and, due to its computational simplicity, can be recommended instead of T. Saaty's hierarchy analysis method in solving applied multicriteria problems.