Coherency: From Outlier Detection to Reducing Comparisons in the ANP Supermatrix

Abstract

The process of coming to a decision with the Analytic Network Process (ANP) and statistical approaches have many similarities. Testing the data is crucial in both frameworks to avoid either using a biased model or obtaining inaccurate predictions. Cross validation is one example of a step used in regression to give an accurate measure of a model’s predictive power. In the ANP there was no way to check the priority vectors in a Supermatrix for outliers or perform any cross validation. The Linking Coherency Index is a way to perform cross validation at the level of the weighted Supermatrix and, in other words, check for “Super-Consistency” to identify outliers among the priority vectors in the weighted Supermatrix. Testing for coherency and updating incoherent priority vectors is an important step to improving the accuracy of the decision model. After identifying incoherent priority vectors, decision makers can: return to the decision making process and update the incoherent priority vector or use a dynamic clustering algorithm to provide a suggested update using data from the linking estimates that were obtained when calculating the Linking Coherency Index. Coherent linking estimates can also be used to reduce the number of needed comparisons in an ANP model which would likely increase its application. Coherency testing is a worthwhile and crucial step in the ANP and should become the norm anytime a decision will be made using the framework.