A common framework for deriving preference values from pairwise comparison matrices
Pairwise comparison is commonly used to estimate preference values of finite alternatives with respect to a given criterion. We discuss 18 estimating methods for deriving preference values from pairwise judgment matrices under a common framework of effectiveness: distance minimization and correctness in error free cases. We point out the importance of commensurate scales when aggregating all the columns of a judgment matrix and the desirability of weighting the columns according to the preference values. The common framework is useful in differentiating the strength and weakness of the estimated methods. Some comparison results of these 18 methods on two sets of judgment matrices with small and large errors are presented. We also give insight regarding the underlying mathematical structure of some of the methods. Pairwise comparison is commonly used to estimate preference values of finite alternatives with respect to a given criterion. This is part of the model structure of the analytical hierarchy process, a widely used multicriteria decision-making methodology. The main difficulty is to reconcile the inevitable inconsistency of the pairwise comparison matrix elicited from the decision makers in real-world applications. We discuss 18 estimating methods for deriving preference values from pairwise judgment matrices under a common framework of effectiveness: the common concepts of minimizing aggregated deviation and correctness in error free cases. The common framework is useful in differentiating the strength and weakness of these methods. For each of these methods, we point out their individual strength in decisional effectiveness. Some comparison results of these 18 methods on two sets of judgment matrices with small and large errors are presented. We also give insight regarding the underlying mathematical structure of some of the methods. We recommend the simple geometric mean method with the stronger feature of distance minimization and the simple normalized column sum method that is based on the simple ideas of commensurate unit and column sum. These two methods have closed-form formulas for easy calculation and good performance on both sets of judgment matrices with small and large errors.
preference values pairwise comparison judgments matrix ratio scale