Tomoe Entani

<p>This study assumes a group of the individuals and aims to obtain each individual inner evaluation from the intuitive judgments by a group of experts. The intuitive judgment is given as a comparison matrix of the multiple criteria and the inner evaluation is obtained as a fuzzy weight vector. Two kinds of the groups are considered: the judgments on the target individual and those by each expert. The inner evaluation of the target individual is simply obtained as the core of the former group. Furthermore, we compare the judgment on the target by an expert with those on all the other individuals by the expert to reflect his/her judgment characteristic. The relation among the judgments in each group is constrained by the inclusion relation and it is relaxed for a fuzzy weight vector. </p>

This paper proposes the model to obtain group decision as the approximation of the individual decisions. Both the group and individual decisions are denoted as the interval weights of alternatives by Interval AHP. The deviations between the individual and group decisions are measured based on the satisfaction and dissatisfaction of each decision maker. S/he is satisfied with the group decision, when his/her decision is included in it. While, s/he is dissatisfied with it, when his/hers does not include it. Then, the group decision is obtained so as to be common to all decision makers' decisions and to maximize and minimize their satisfactions and dissatisfactions, respectively.

When the decision maker gives a pairwise comparison matrix on alternatives, their priority weights are obtained by Analytic Hierarchy Process (AHP). In a group decision making, we assume that each group member gives his/her own pairwise comparison matrix. In this paper, a method for obtaining the interval priority weights of alternatives as the collective evaluation from the given many matrices is investigated. We basically presume that the individual matrices are the possible realizations of the collective interval priority weights in order to reflect all group members' opinions and their widths are minimized. However, as is often in the real world, the individual opinions are not always similar so that the collective intervals might be extremely wide. To avoid this, we relax the presumption by introducing the deviations for the individual intervals from the collective ones. Then the problem is formulated as the biobjective programming problem which minimizes the widths of the collective intervals and the deviations from individual intervals.