AN ANALYSIS OF RANK PRESERVATION AND REVERSAL IN THE ANALYTIC HIERARCHY PROCESS

Abstract

The Analytic Hiemrchy Process (AHP) is an extensively used tool for setting up the rank order of the alternatives in multiple criteria decision making problems. AHP has been widely applied in practice with illconsistent paired comparison matrices. In this case,however, the rank order of the alternatives does not remain stable, a rank reversal may occur. In this paper it is demonstrated that this phenomenon is inherent in AHP even if the matrix is slightly inconsistent only. Conditions and regions of such a rank reversal are also given.