Mean values as nondominated multicriterial points

Journal of Multi-Criteria Decision Analysis. 2024. Vol. 31. No. 1-2. Article e1824.

Vladislav V. Podinovski, Nelyubin A.

In this paper, we introduce new notions of mean values based on ideas of multicriteria optimization. The distances between the current point to all points in the sample are regarded as elements of a vector estimate. Such vector estimates are usually scalarized, e.g., by taking the sum of all components. In contrast, we introduce preference relations on the set of all such vectors, based on the information about the preferences of the decision maker who could be a statistician, analyst or researcher. Such preference relations reflect the distances between points, including the case in which all distances are equally important. We define the mean values as the points whose corresponding vector estimates are nondominated with respect to the defined preference relation, and investigate their properties. Such mean values turn out to be multi-valued. We further explore the relationship between the new notions of mean values with their conventional definitions and suggest computational approaches to the calculation of the suggested new means. We also outline generalizations of the suggested approach to the case of multidimensional data.

Keywords: многокритериальная оптимизация, multicriteria optimization, средние величины, недоминируемые точки, preference relations, отношения предпочтения, mean values, nondominated points

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