Decision making problems where possible choices are evaluated by several numeric criteria and preferences of the decision maker are described by a binary relation are considered. Under certain rational assumptions, characterizing reasonable behaviour of the decision maker, it was proven that the selected choices must be Pareto optimal. However, in most cases the Pareto set is too wide for the decision maker to determine the final choice directly. Axiomatic approach to Pareto set reduction aims at simplifying the task of selecting the final choice from the Pareto set by narrowing it with the use of the decision maker's individual preferences. The extent to which the Pareto set can be reduced is studied. It is shown that if accounting for the decision maker's preferences makes it possible to narrow the Pareto set to a single choice, then there must exist a linear combination of the criteria that attains maximum at that choice. As this condition is quite strong, in practice one should not expect that the axiomatic approach would narrow the Pareto set down to a single choice. The final choice should always be made by the decision maker.

Authors: O. V. Baskov, V. A. Smirnova

Direction: Informatics, Computer Technologies And Control

Keywords: Multicriteria optimization, Pareto set reduction, axiomatic approach

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