Multi-criteria decision making with a special type of information about importance of groups of criteria

An axiomatic approach for solving a multi-criteria decision making problem is studied in the paper, which generally allows reducing a set of Pareto optimal solutions. The information about criteria in the problem is represented as the decision maker judgments of a special type. The judgments have a clear behavior interpretation and can be used in various decision problems. It is shown in the paper how to combine the judgments and to use them for reducing the Pareto set when they are provided by several decision makers. Two global criteria of decision making are introduced for comparing of decision alternatives. The first criterion based on the lower expectation, the second one is based on determining the belief and plausibility functions in the framework of Dempster-Shafer theory and uses the “threshold” probability for the final decision making. The numerical examples illustrate the proposed approach.