Linking Disjoint Supermatrices and Criteria Clusters

Abstract

An axiom of the Analytic Network Process (ANP) requires the elements being considered to be strongly connected in order to obtain a meaningful priority vector. A simple example demonstrates the issues that can arise when a decision contains disjoint clusters within the Supermatrix. From the example it can be observed that the necessary information to complete additional linking pin comparisons would have already been collected; and by performing linking pin comparisons a decision maker can convert a disjoint Supermatrix into a strongly connected Supermatrix. The linking process is summarized in five steps and provided in the general form. This linking comparison methodology exploits the fundamental advantages of pairwise comparisons and can also be used to weight the criteria clusters within a decision network. Linking pin comparisons performed at the level of a criterion of a single alternative with respect to another criterion of that same alternative can be used to obtain the criteria cluster weights. Linking pin comparisons at this level can reduce the decision maker's cognitive burden in comparison to totality comparisons. The ability to strongly connect an otherwise disjoint Supermatrix and reduce the decision maker's cognitive burden demonstrates the usefulness of linking pin comparisons in ANP decision models.

A Hybrid ANP Method for Evaluation of Government Data Sustainability

“…However, the results are neither perfect nor acceptable, which is because there is no satisfactory solution if the graph is not strongly connected. In the paper of Orrin and Guoqing [42], an example is cited to demonstrate that a decision-maker can form a disjointed supermatrix by following the process of ANP. Zammori and Gabbrielli [16] provide a typical example to explain the fatal problem caused by a black hole in the ANP network (weakly connected network).…”