RANK GENERATION, PRESERVATION, AND REVERSAL IN THE ANALYTIC HIERARCHY DECISION PROCESS

TLDR

Decision making seeks the best alternatives by evaluating multiple criteria, and the analytic hierarchy process aids this by structuring complex decisions, but its arithmetic must correctly preserve or alter rankings when alternatives change. The study aims to demonstrate how absolute versus relative measurement affects rank preservation in the analytic hierarchy process. The authors analyze the impact of replicating or nearly replicating alternatives on their ranking. The results show that absolute measurement preserves rankings, while relative measurement changes rankings only through structural dependence on criteria and alternatives.

Abstract

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.