Mean values as nondominated multicriterial points

IF 1.9 Q3 MANAGEMENT Journal of Multi-Criteria Decision Analysis Pub Date : 2023-11-13 DOI:10.1002/mcda.1824
Vladislav V. Podinovski, Andrey P. Nelyubin
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Abstract

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, for example, 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 generalisations of the suggested approach to the case of multidimensional data.

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作为非支配多标准点的平均值
在本文中,我们根据多标准优化的思想引入了新的平均值概念。当前点与样本中所有点之间的距离被视为矢量估计值的元素。这种矢量估计值通常是标量化的,例如,取所有分量之和。与此相反,我们根据决策者(可能是统计人员、分析师或研究人员)的偏好信息,在所有此类向量集合上引入偏好关系。这种偏好关系反映了各点之间的距离,包括所有距离都同等重要的情况。我们将平均值定义为其相应的向量估计值相对于所定义的偏好关系而言是非主流的点,并研究其特性。结果表明,这种均值是多值的。我们进一步探讨了均值的新概念与其传统定义之间的关系,并提出了计算所建议的新均值的方法。我们还概述了建议方法在多维数据情况下的一般应用。
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来源期刊
CiteScore
4.70
自引率
10.00%
发文量
14
期刊介绍: The Journal of Multi-Criteria Decision Analysis was launched in 1992, and from the outset has aimed to be the repository of choice for papers covering all aspects of MCDA/MCDM. The journal provides an international forum for the presentation and discussion of all aspects of research, application and evaluation of multi-criteria decision analysis, and publishes material from a variety of disciplines and all schools of thought. Papers addressing mathematical, theoretical, and behavioural aspects are welcome, as are case studies, applications and evaluation of techniques and methodologies.
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