An algorithm of Pareto set reducing based on arbitrary finite collection of “quanta” of information

In this paper, in the framework of the axiomatic approach, developed by the author over the past three decades, four axioms of “reasonable” choice, which outline a sufficiently broad class of multicriteria choice problems, are accepted. To narrow down the Pareto set is used some numerical information on the DM's preference relation. A method to reduce the Pareto set using an arbitrary consistent finite collection of such information is developed. The method is based on an algorithm that generates a new vector criterion with minimal number of components. The Pareto set with respect to new vector criterion gives the desired narrowing of the initial Pareto set.