An optimization approach to estimating ratios in Saaty's priority theory

The paper concerns ranking factors using the pairwise comparison method in the sense of AHP. To approximate a judgement matrix the logarithmic least square approach is used, what results in normal equations. Cases with multiple experts, lacking and fuzzy judgements are considered. Depending on number of judgements and character of data the normal equation set has one or more degrees of freedom. Therefore a general technique to solve linear equations should be applied. An approach based on a generalized pseudoinverse is recalled and an optimization based method is introduced, developed and compared with the former one. Exemplary numerical calculations are included. Possible extensions are indicated.