Abstract
This paper investigates a decision problem of evaluating alternatives under multi-criteria. For several terms, the individual evaluations of each alternative under each criterion are recorded repeatedly. Then, as a final decision the collective evaluation over all terms and all criteria is obtained. In order to deal each term and criterion independently, the aggregations of individual evaluations are done by the approximation, differently from by the summation. The first step is to aggregate evaluations over all terms. From the possibility view, the aggregation is obtained as the upper approximation of individual evaluations so that the varieties depending on terms are reflected in an interval. The second step is to aggregate the obtained interval evaluations under over all criteria. From the core evaluations view, the aggregations are based on the lower approximation. Depending on the viewpoints of criteria and alternatives, two aggregation models are proposed.
