The balance space approach to multicriteria decision making – involving the decision maker

This paper is a contribution to earlier investigations made in order to apply the balance set approach for multicriteria optimization problems. The initial point of the investigation is the minimal deviation from optimality of the individual objectives (so-called ‘ideal point’). The author emphasizes the active role of the decision maker (DM). In fact, the DM can specify proportions among the deviations as a weights vector according to his considerations. The main results are necessary and sufficient conditions for the balance set to be exhaustive. In this case, by means of multiplying a vector weight from the DM with its apportioned balance number, a balance point is attained. It is necessary to mention that the balance space theory resembles much of the Charnes and Cooper approach, which is based on the concepts of ideal point and deviation from that point.