Pareto set reducing based on information about the DM’ preference relation of point-set type

The paper deals with multicriteria choice model, which includes a set of variants, a numerical vector-valued criteria, and an asymmetric DM’s preference relation. Set of selected variants is considered as a solution of the multicriteria choice problem. We assume that some reasonable axioms have been accepted. When the preference relation is known only partially, we cannot construct the set of selected variants but are able to get some upper estimate for this set based on information about the DM’s preference relation. Suppose that information on the preference relation has a point-set type. This means that the DM are ready to lose in several groups of criteria in order to obtain a gain in other group of criteria. By using this information we should form new vector criterion and build new reduced Pareto set that represents a more precise upper estimate for unknown set of selected variants than the initial Pareto set.