An efficient nonlinear programming method for eliciting preference weights of incomplete comparisons

The Analytic Hierarchy Process (AHP) which was developed by Saaty is a decision analysis tool. It has been applied to many different decision fields. Acquiring Pairwise Comparison Matrices (PCM) is the main step in AHP and also is frequently used in other multi-criteria decision-making methods. In a real problem when the number of alternatives/criteria to be compared is increased, the number of Pairwise Comparisons (PC) often becomes overwhelming. Since the Decision Maker’s (DM) performance in representing the relative preferences tends to deteriorate in such cases, it is preferred to gather fewer data from each individual DM in the form of pairwise comparisons. Missing values in Pairwise Comparison Matrices (PCM) in AHP is a spreading problem in areas dealing with great or dynamic data. The aim of this paper is to present an efficient mathematical programming model for estimating preference vector of pairwise comparison matrices with missing entries.