Building Consistent Pairwise Comparison Matrices over Abelian Linearly Ordered Groups
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Transitive pairwise comparison matrices over abelian linearly ordered groups
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
A different perspective on a scale for pairwise comparisons
Transactions on computational collective intelligence I
A Semiring-based study of judgment matrices: properties and models
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
| Hi-index | 0.00 |
In a multicriteria decision making context, a pairwise comparison matrix A = (aij) is a helpful tool to determine the weighted ranking on a set X of alternatives or criteria. The entry aij of the matrix can assume different meanings: aij can be a preference ratio (multiplicative case) or a preference difference (additive case) or aij 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. © 2009 Wiley Periodicals, Inc.