A loss function approach to group preference aggregation in the AHP

The Analytic Hierarchy Process (AHP) is a useful method in aggregating group preference. We suggest a new method that uses consistency ratio as group evaluation quality. For this method, we introduce Taguchi's loss function. We also develop an evaluation reliability function to derive group weight. Lastly, we perform four experiments in order to confirm validity of this method. 1. Introduction The AHP as a growing field in both its theoretical and applied ramifications has been applied widely in decision making. One of the topics on which research concentrates is the problem of group judgments aggregation and consistency ratio. The previous group aggregation methods keeps Saaty's rule that consistency ratio of individual pairwise comparison should be less than 0.1. That is, in aggregating individual judgments to a group opinion, one takes only individual judgments whose consistency ratio is less than 0.1. However, judgments are frequently inconsistent, and practically, pairwise comparison matrices rarely satisfy the consistency criterion. Thus these methods tend to ignore many information of evaluation by using Saaty's consistency ratio. While previous methods dealt with weight of each evaluator, there have been no studies that tried to aggregate group priority by using weight of a group unit in aggregating individual judgment. In order to overcome such problems, we introduce the concept of Taguchi's loss function and develop a loss function approach, which is a new method for improving group judgments aggregation. The loss of evaluation quality will be used as the weight of group in aggregating group judgments. We call this method the Weighted After Geometric Mean Method (WAGMM) and the Weighted After Arithmetic Mean Method (WAAMM) for convenience.