Abstract
In multicriteria decision making, the pairwise comparisons are an useful starting point for determining a ranking on a set X = {x 1,x 2,..., x n } of alternatives or criteria; the pairwise comparison between x i and x j is quantified in a number a ij expressing how much x i is preferred to x j and the quantitative preference relation is represented by means of the matrix A = (a ij ). In literature the number a ij can assume different meanings (for instance a ratio or a difference) and so several kind of pairwise comparison matrices are proposed. A condition of consistency for the matrix A = (a ij ) is also considered; this condition, if satisfied, allows to determine a weighted ranking that perfectly represents the expressed preferences. The shape of the consistency condition depends on the meaning of the number a ij . In order to unify the different approaches and remove some drawbacks, related for example to the fuzzy additive consistency, in a previous paper we have considered pairwise comparison matrices over an abelian linearly ordered group; in this context we have provided, for a pairwise comparison matrix, a general definition of consistency and a measure of closeness to consistency. With reference to the new general unifying context, in this paper we provide some issue on a consistent matrix and a new measure of consistency that is easier to compute; moreover we provide an algorithm to check the consistency of a pairwise comparison matrix and an algorithm to build consistent matrices.
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Cavallo, B., D’Apuzzo, L., Marcarelli, G. (2010). Pairwise Comparison Matrices: Some Issue on Consistency and a New Consistency Index. In: Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R., Kacprzyk, J. (eds) Preferences and Decisions. Studies in Fuzziness and Soft Computing, vol 257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15976-3_7
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DOI: https://doi.org/10.1007/978-3-642-15976-3_7
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