A method for dealing with inconsistencies in pairwise comparisons. (English) Zbl 1067.90070

Summary: The Pairwise Comparison method is a powerful inference tool for assessing the relative importance of a set of items. Formally, its objective is to make compatible decision maker’s assignments (paired comparison) with properties needed for obtaining an overall rank. In this paper, we propose a distance-based framework for analysing this kind of compatibility. In this context, goal programming is proposed as an attractive and flexible tool.


90B50 Management decision making, including multiple objectives
90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI


[1] Crawford, G, The geometric Mean procedure for estimating the scale of judgement matrix, Mathematical modelling, 9, 227-334, (1987) · Zbl 0624.62108
[2] Chu, M.T, On the optimal consistent approximation to pairwise comparison matrices, Linear algebra and its applications, 272, 155-168, (1998) · Zbl 0905.62005
[3] Gass, S.I, Tournaments, transitivity and pairwise comparison matrices, Journal of the operational research society, 49, 616-624, (1998) · Zbl 1131.90381
[4] González-Pachón, J; Romero, C, Distance-based consensus methods: A goal programming approach, Omega, 27, 341-347, (1999)
[5] González-Pachón, J; Rodrı́guez-Galiano, M.I; Romero, C, Transitive approximation to pairwise comparison matrices by using interval goal programming, Journal of the operational research society, 54, 5, 532-538, (2003) · Zbl 1070.90053
[6] Herman, M.W; Koczkodaj, W, A Monte Carlo study of pairwise comparison, Information processing letters, 57, 25-29, (1996) · Zbl 1004.68550
[7] Ignizio, J.P; Cavalier, T.M, Linear programming, (1994), Prentice-Hall New Jersey
[8] Koczkodaj, W; Orlowski, M, Computing a consistent approximation to a generalized pairwise comparisons matrix, Computers and mathematics with applications, 37, 79-85, (1999) · Zbl 0936.65057
[9] Roberts, F.S, Measurement theory, (1979), Addison-Wesley Reading, MA
[10] Romero, C, Handbook of critical issues in goal programming, (1991), Pergamon Press Oxford · Zbl 0817.68034
[11] Romero, C, Extended lexicographic goal programming: a unifying approach, Omega, 29, 63-71, (2001)
[12] Saaty, T.L, The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
[13] Wei, T.H, The algebraic foundations of ranking theory, (1952), Cambridge University Press London
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.