Linking validation: A search for coherency within the Supermatrix

The consistency check within each pairwise comparison matrix is an important step in an Analytic Network Process (ANP) decision. In an ANP network there is both the ability and the need to test for additional levels of consistency or coherency among the priority vectors. Examples are used to highlight cases where a Supermatrix with priority vectors that were obtained from either perfect or nearly perfect consistent pairwise comparison matrices generates suboptimal decisions. Simulations are used to further demonstrate the frequency of these occurrences in general ANP networks. A form of cross validation within the Supermatrix called linking validation is developed and demonstrated. The linking validation method allows decision makers to use the priority vectors within the Supermatrix to validate other priority vectors within the Supermatrix. The linking validation method involves generating linking estimates. The linking estimates are compared against each other to identify the most incoherent priority vector by calculating the Linking Coherency Index (LCI) scores. The decision maker can then update the specified priority vector and repeat this process until the LCI-score for every linking estimate is below the given threshold. The use of linking validation to test for coherency further improves the validity of ANP models.