Achieving Matrix Consistency in AHP through Linearization

Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pairwise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent- and sometimes the level of consistency may be unacceptable. Dif-ferent methods have been used in the literature to achieve consistency for an inconsistent matrix. In this paper we use a linearization technique that provides the closest consistent matrix to a given inconsistent matrix using orthogonal projection in a linear space. As a result, consistency can be achieved in a closed form. This is simpler and cheaper com-pared to methods that relying on optimization, which are iterative by nature. We apply the process to a real-world decision-making problem in water supply management. Key words: analytic hierarchy process, decision-making, linearization, leakage man-agement AMS Subject Classification: 15B48, 90B50, 41A99