A scale-extending method for constructing the judgement matrix in the analytic hierarchy process

The judgement matrices in the Analytic Hierarchy Process often do not pass the consistency check, which leads to failure in practical decision-making. The problem has not been completely solved. The examples in this paper show that the main factor of the consistency checking error of the judgement matrix is a fault which exists in the traditional method for constructing a judgement matrix. It makes the judgement scales rigid. A new method for judgement matrices which are always fully consistent by a changed weight vector can be found. The new method enhances the reliability of decision-making of AHP, and makes the AHP simple and easy to use.