A dynamic clustering method to improve the coherency of an ANP Supermatrix

When making decisions with the Analytic Network Process, coherency testing is an important step in the decision making process. Once an incoherent priority vector is identified it can either be costly or in some cases next to impossible to elicit new pairwise comparisons. Remarkably, there is useful information in the linking estimates that one may have already calculated and used in one of the approaches to measure the coherency of the Supermatrix. A dynamic clustering method is used to automatically identify a cluster of coherent linking estimates from which a new coherent priority vector can be calculated and used to replace the most incoherent priority vector. The decision maker can then accept or revise the proposed new and coherent priority vector. This process is repeated until the entire Supermatrix is coherent. This method can save decision makers valuable time and effort by using the information and relationships that already exist in a weighted Supermatrix that is sufficiently coherent. The method is initially motivated and demonstrated through a simple straightforward example. A group of conceptual charts and a figure provide a visual motivation and explanation of the method. A high level summary of the method is provided in a table before the method is presented in detail. Simulations demonstrate both the application and the robustness of the proposed method. Code is provided, as supplementary material, in the programming language R so the method can be easily applied by the decision maker.