A Fuzzy Weight Vector From a Group of Crisp Pairwise Comparison Matrices

This study considers one of the decision problems, which is to assign numbers to multiple items based on our judgments. In this paper, a fuzzy weight vector is obtained from a group of the crisp comparison matrices which are given intuitively, since a fuzzy number is more suitable to represent our thinking than a crisp number. It is based on the idea that the result could be better if a comparison matrix is supplemented by the other comparison matrices on the same items. In this sense, the goal of this study is not to find a consensus, which is often discussed in group decision making literature. The proposed methods consider both relations among the comparisons in each comparison matrix and among the comparison matrices simultaneously so that there is no aggregation process. They derive an interval weight vector as a level set of fuzzy weight vector from a group of comparison matrices. Then, the membership function of the fuzzy weight vector is estimated from the obtained interval weight vectors.