Rank Generation, Preservation, and Reversal in the Analytic Hierarchy Decision Process

ABSTRACT Decision making has the objective of finding the best alternative or set of alternatives by considering a number of goals, objectives, criteria, competitors, and other important factors. The analytic hierarchy process is a decision aid used to assist a decision maker in sorting out the complexity of a decision problem and making use of his or her judgments. A decision maker must be assured that the arithmetic operations of any such decision process are the right ones—that they surface the correct ranking and values of the alternatives and preserve or alter ranks appropriately when new alternatives are added or deleted. In this paper it will be shown that with absolute measurement, rank always is preserved, with relative measurement, rank changes with nspect to scveral criteria only because of the structural dependence (involving both numbers and measurements) of criteria on alternatives. A discussion of the effect on rank of replicas and near replicas of the alternatives also is given.