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Efficient weight vectors from pairwise comparison matrices
Authors:Sándor Bozóki  János Fülöp
Institution:1. Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Budapest 1518, P.O.?Box 63, Hungary;2. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Hungary;3. Institute of Applied Mathematics, John von Neumann Faculty of Informatics, Óbuda University, Hungary
Abstract:Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and strictly better in at least one position. A weight vector is weakly efficient if the pairwise ratios cannot be improved in all non-diagonal positions. We show that the principal eigenvector is always weakly efficient, but numerical examples show that it can be inefficient. The linear programs proposed test whether a given weight vector is (weakly) efficient, and in case of (strong) inefficiency, an efficient (strongly) dominating weight vector is calculated. The proposed algorithms are implemented in Pairwise Comparison Matrix Calculator, available at pcmc.online.
Keywords:Multiple criteria analysis  Pairwise comparison matrix  Pareto optimality  Efficiency  Linear programming
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