Optimisation Approach to Dealing with Saaty's Inconsistency

We revisit the issue of the AHP method, wherein it often happens that an evaluation of a matrix based on Saaty's scale is inconsistent. The inconsistency of the matrix originates from ill-defined pairwise comparisons provided by a decision-maker. The measurement of the inconsistency is very well known. The less discussed issue is fixing the original data to achieve the required consistency. It is not expected from the decision-maker to re-evaluate the comparisons because: 1) the decision-maker is not available anymore, 2) the decision-maker is not capable of making such adjustments that would lead to inconsistency improvement. We propose our own approach based on a nonlinear optimisation model. We show how to adjust the matrix values to preserve the original information contained in the pairwise comparison while achieving acceptable inconsistency. We compare our approach with the earlier ones in the end.