Interval Weights and Consistency Check of Judgment Matrix in the Analytic Hierarchy Process

Traditional methods can only educe strict weights from a judgment matrix in the analytic hierarchy process. To make the solution be more flexible, an interval weight vector is obtained, which is achieved through linear programming method in this paper. Meanwhile, the optimal objective value of the LP model implies consistency of the judgment matrix. Consequently, it can be used to process consistency check. By simulation computing, statistical analysis on the correlation between this check method and traditional method by CR value is made. The result indicates that the correlation between the two methods is significant. Finally an example is given.