A supplement to saaty's consistency theory of judgment matrix in the analytic hierarchy process

In order to supplement the saaty's consistency theory of judgment matrix, the experts' psychological expectation of the comparative scale values is studied. The omission of the saaty's consistency theory is analyzed. An innovative consistency definition of judgment matrix is proposed. A matrix adjustment method is developed from this definition. This method is compared with the existing methods from two aspects which contain overall consistency of matrix and inconsistency of matrix element, to verify the rationality and necessity of the method. In the end, the supplemented and original theories are combined and expanded to judgment matrix consistency adjustment under general circumstances, so that the existing judgment matrix consistency theory is improved.