A concept of compromise solutions and the method of the displaced ideal

Abstract In problems with multiple noncommensurable objectives, finding the set of nondominated solutions can be considered a sound first step of any decision making methodology. Such a set could however be too large to allow the decision maker to choose the final solution safely. So an effort is made to help the decision maker to reduce the set of nondominated solutions by eliminating some “obviously bad” solutions. Several complementary ways of reducing the nondominated set are discussed: weight space decomposition, fuzzy weight assessment and the ideal solution displacement. A new concept of the weight of importance based on attribute entropy measurement is introduced. Numerical examples are given throughout the text.