Mean values: a multicriteria approach. Part III

A new approach to defining mean values based on the ideas of multicriteria optimization was proposed and developed previously; see the papers [4] and [5]. The distances between the current point and the sample points were treated as components of a vector estimate. The conventional approach to defining mean values involves the scalarization of vector estimates: they are replaced, e.g., by the sums of their squared components. On the contrary, we proceeded from comparing vector estimates by preference. Several types of mean values corresponding to different amounts of information about preferences were considered. The properties of such mean values were investigated, and computational methods for constructing them were given. However, in the case of equally important criteria, the method turns out to be approximate and rather computationally intensive. In this paper, we present an exact and efficient numerical method for constructing a set of mean values of the specified type. The method is illustrated by a computational example.