Fuzzy Approach for Group Assessment Based on the Consistency of Individual Judgments

Abstract

In this study, we propose a method to assign the weights to the viewpoints for the assessment of an item. The weight vector is obtained from the pairwise comparison matrix of the item on the viewpoints given by a decision maker. The comparison matrix is incomplete in the sense of the missing comparisons and inconsistency among the comparisons. As for the missing comparisons, we assume the inclusion relation between the given comparison and the obtained interval weights as in Interval Analytic Hierarchy Process (AHP). As for the inconsistency, we assume the comparison matrices of the other items by the decision maker and find out his/her consistency degree. Moreover, the incompleteness motivates us to consider the other decision makers who give the comparison matrices of the item. In other words, all the given comparisons are reliable since a decision maker need not give the comparisons if s/he is not confident in it. It is reasonable that the weight vector of the item should be the core of those of all the decision makers. The weight vector of each decision with a higher consistency degree is more preferable. However, there is a trade-off among the consistency degree, the inclusion relation, and the core condition. We introduce a fuzzy approach, which simultaneously minimizes the relaxations of the inclusion relation and the core condition and maximizes the consistency degree, to obtain the weight vector of the target item.