An experimental measurement of contradictory judgement matrices in AHP

Abstract

Often Multi Criteria Decision Making (MCDM) techniques are used to assist in deciding a best choice, or alternative, in many different types of environment. Analytic Hierarchy Process (AHP) is one of the most popular MCDM technique used in variety of domains. It not only generates numerical order of alternatives that indicates an order of preference among them but also reflect there intensity or cardinal preference among them. Despite its advantages and popularity, AHP is often criticized in the literature for many reasons. One such reason is the Consistency Index which it requires to compute for every judgement matrix. As a result of this, it allows the consideration of Contradictory matrices for which no true ordinal ranking satisfying all the relations contained in the judgement matrix can exist. This paper shows the results of an experimental analysis as an attempt to measure the magnitude of this problem. Results show that as the order of pair wise comparison matricx increases the intensity of this problem also increases.