Improving AHP consistency

In the implementation of both, AHP excel template as well as AHP online software, inconsistent judgments are highlighted and recommendations for consistent judgments are given.  How it is done, and what is the method behind?

The method is based on Saaty’s article “Decision-making with the AHP: Why is the principal eigenvector necessary“. European Journal of Operational Research 145 (2003) 85–91. He describes three methods how to transform a positive reciprocal matrix to a near consistent matrix.

In my implementation I construct the matrix εij = aij wj/wi to identify the three judgments for which εij is farthest from one. In Saaty’s paper it is shown as table 3, in my excel template it is called Consistency Error Matrix.  As I have to do it on each individual input sheet, I use as an approximation the RGMM (row geometric mean method) results, before calculating the eigenvector solution in the summary sheet.

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