Mean values: a multicriteria approach. Part III

Control Sciences. 2024. No. 1. P. 13–17.

Nelyubin A. P., Podinovskiy V. V.

A new approach to defining mean values based on the ideas of multicriteria optimiza-tion 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 con-ventional 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 differ-ent amounts of information about preferences were considered. The properties of such mean val-ues 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 computa-tionally intensive. In this paper, we present an exact and efficient numerical method for construct-ing a set of mean values of the specified type. The method is illustrated by a computational ex-ample.

Keywords: criteria importance theory, теория важности критериев, multicriteria choice problems, задачи многокритериального выбора, средние величины, preference relations, отношения предпочтения, mean values

Publication based on the results of: Models of data analysis and decision making in the socio-economic sphere (2024)