Validation Examples for the Analytic Hierarchy Process and the Analytic Network Process

Key words : Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), validation in decision making Abstract Two main ideas are illustrated in this paper: validating the pairwise comparison process and the fundamental scale used in the Analytic Hierarchy Process (AHP) for decision making and validating the Analytic Network Process (ANP) for decision making with dependence and feedback, the extension of the AHP to network structures and the supermatrix. The Saaty compatibility index is used to show how close derived priorities are to actual values against which we wish to compare them. Examples like the ones in this paper, and there are many more that were not included here, encourage us to believe the AHP and the ANP are valid when applied in real life problems. INTRODUCTION The story that I want to tell you is about using the human mind as a measuring instrument. We need to be able to validate such measures and the best we can do is to apply our method to things for which we have measurements and compare our results with the actual measures. Measurable things are known as tangibles. We have many examples of validating the Analytic Hierarchy Process (AHP) in this way that show the mind is a good measuring instrument. We shall start by showing two AHP validation examples. Then we shall move to validation examples for the Analytic Network Process (ANP). The AHP and ANP are descriptive psycho-physical theories that aim to use judgments about factors in the real world to give back priorities. If they are tangibles, we use judgments about their relative magnitudes to derive relative values that we can then compare to actual measures, normalized. If they are intangibles, we still use judgments to derive the relative values (Saaty, 2000). Thus the AHP is a descriptive theory rather than a prescriptive or normative theory. Any truly scientific theory is descriptive: for example, the physics equation relating the time it takes a particle to fall from a prescribed height. The AHP and ANP can be used as a tool for prediction, a basic requirement in science for a theory to be reliable in terms of cause and effects.