Ultimate possibilities of the Рareto set reduction based on quanta of fuzzy information

The problem of multicriteria choice with a fuzzy preference relation is considered, the main objects of which are a set of feasible alternatives, a numerical vector criterion and the fuzzy preference relation of the decision maker (DM). Concepts of a fuzzy vector space, a polyhedral fuzzy set and the distance between convex fuzzy sets and cones are used. To reduce the Pareto set the ultimate possibilities of information about the fuzzy preference relation in the form of quanta of information set are studied. It is proved that in a sufficiently wide class of above problems with a finite set of quanta of fuzzy information, one can arbitrarily accurate approximate an initially unknown fuzzy set of nondominant elements.