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Mean Values: A Multicriterial Analysis

In: Data Analysis and Optimization

Author

Listed:
  • Vladislav V. Podinovski

    (National Research University Higher School of Economics)

  • Andrey P. Nelyubin

    (Mechanical Engineering Research Institute RAS)

Abstract

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. 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.

Suggested Citation

  • Vladislav V. Podinovski & Andrey P. Nelyubin, 2023. "Mean Values: A Multicriterial Analysis," Springer Optimization and Its Applications, in: Boris Goldengorin & Sergei Kuznetsov (ed.), Data Analysis and Optimization, pages 257-270, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-31654-8_17
    DOI: 10.1007/978-3-031-31654-8_17
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