Subjective Geometry for Problem Modeling in the Analytic Hierarchy/Network Processes

Abstract

This paper is in memory of Professor Thomas L. Saaty, who died on the 14th of August 2017. In a problem-solving process, the first step is to model a real-world problem. The modeling effort is one of the hardest parts of the process, and there is no universal way to do it. The initial step involves structuring the problem and obtaining a simplified problem so that any multi-criteria or statistical models can be applied. This paper intends to explain the modeling process through subjective geometry. Although creative thinking is critical in developing the hierarchies and networks in the Analytic Hierarchy or Network Process (AHP/ANP), models from business management and information theories can supply a verified ready-to-use relationship among elements and their clusters. We hope the exploration offers a guideline for utilizing the AHP/ANP in more detail.