A distance-metric methodology for the derivation of weights from a pairwise comparison matrix

Abstract

A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison.

Keywords:

• goal programming
• multiobjective programming
• pairwise comparison
• analytic hierarchy process

Acknowledgements

This research was partly funded by the European Commission 5th Framework project QLK5-1999-01273 (MOFISH).