A note on the pseudoinverse approach to estimating ratios

The paper concerns the pairwise-comparison method used in Analytic Hierarchy Process introduced by Saaty in order to rank a finite number of attributes, factors or criteria in multi-criteria group decision making. There are three main approaches to estimate judgment matrices, namely the eigenvalue, the least squares and the logarithmic least squares method. The latter is used because it allows to handle judgment matrices with ‘lacking’ judgments, and it is consistent with the maximal likelihood estimator approach. This method produces a system of so called normal linear equations, which in general case can be solved using the pseudoinverse approach. The method presented in this paper is equivalent to the pseudoinverse approach, and leads to a solution that is geometrically normalized. Numerical examples are included. Possible extensions, remarks and comments are presented.