Clustering and reference value for assessing influence in analytic network process without pairwise comparison matrices: Study of 17 real cases

The analytic network process (ANP) is a well-known multi-criteria decision method that uses pairwise comparison matrices to assess the influence among elements and clusters. This method requires the participation of experts who need to answer a large number of questions. A recent paper proposes using Decision-Making Trial and Evaluation (DEMATEL) scales in ANP to assess influences and suggests the possibility of grouping all elements into a single cluster. This rise the following questions that this paper seek to answer: if no comparison matrices are used in ANP, how similar are the results, whether clusters are used or not, to the original results with ANP using pairwise matrices? Why should or should not one or several groups be used in ANP? How much does the result change when considering multiple groups versus a single group? Does the variation of questions compensate for the variation of the results? How should the evaluation of influences and the use of the scale be approached depending on whether there are one or several groups? For this purpose, published cases solved with ANP have been reviewed and solved without comparison matrices, with the original clustering and with a single cluster, using four different models for each case study. The results show that clustering does influence the results. It should also be noted that the use of clustering helps to identify the elements of the decision problem. Additionally, this work includes the compilation of 17 cases matrices which can be used in further studies