Multi-Criteria Problems with Groups of Criteria Ordered by Importance (II). Decision Rules

For multi-criteria decision-making problems, by analogy with qualitative probability, the concepts of complete and partial qualitative importance are introduced as binary relations satisfying certain postulated properties. A new definition of a non-strict preference relation on the set of decision alternatives, generated by qualitative importance, is proposed, and its properties are examined. Analytical rules for pairwise comparison of alternatives in terms of preference are provided. The new preference relations are compared with those developed earlier for problems in which only individual criteria are initially ordered by importance. It is shown that when all criteria are completely ordered by importance, the two preference relations coincide.