A general unified framework for pairwise comparison matrices in multicriterial methods
✍ Scribed by B. Cavallo; L. D'Apuzzo
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 186 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0884-8173
No coin nor oath required. For personal study only.
✦ Synopsis
In a multicriteria decision making context, a pairwise comparison matrix A = (a ij ) is a helpful tool to determine the weighted ranking on a set X of alternatives or criteria. The entry a ij of the matrix can assume different meanings: a ij can be a preference ratio (multiplicative case) or a preference difference (additive case) or a ij belongs to [0, 1] and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix A has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix.