Analytic Hierarchy Process

Abstract

The Analytic Hierarchy Process (AHP) is a theory of relative measurement of intangible criteria. With this approach to relative measurement, a scale of priorities is derived from pairwise comparison measurements only after the elements to be measured are known. The ability to do pairwise comparisons is our biological heritage and we need it to cope with a world where everything is relative and constantly changing and thus, there are no fixed standards to measure things on. In traditional measurement, one has a scale that one applies to measure any element that comes along that has the property the scale is for, and the elements are measured one by one, not by comparing them with each other. In the AHP, paired comparisons are made with judgments using numerical values taken from the AHP absolute fundamental scale of 1 to 9. A scale of relative values is derived from all these paired comparisons and it also belongs to an absolute scale that is invariant under the identity transformation like the system of real numbers. The AHP is useful for making multicriteria decisions involving benefits, opportunities, costs, and risks. The ideas are developed in stages and illustrated with examples of real-life decisions. The subject is transparent and easy to understand why it is done the way it is along the lines discussed here. The AHP has a generalization to dependence and feedback; the Analytic Network Process (ANP) is not discussed here. Among the most important decisions made in society today are those relating to the life and health of people. How does one make a decision when faced with many conflicting factors that determine the best choice among the available alternatives of that decision? Most of these factors may be intangibles and the choice is not simply a matter of making financial trade-offs. How does one pool the judgments of doctors and other experts with their varying degrees of expertise to obtain the best decision? Who should bear the costs, and how much control should there be, what should be legal and what should not, who should receive an organ in transplant operations, and what is the best treatment for a certain type of disease? If we have standard measurements for how average people score on medical tests and