{"title":"Mean values as nondominated multicriterial points","authors":"Vladislav V. Podinovski, Andrey P. Nelyubin","doi":"10.1002/mcda.1824","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":45876,"journal":{"name":"Journal of Multi-Criteria Decision Analysis","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multi-Criteria Decision Analysis","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mcda.1824","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MANAGEMENT","Score":null,"Total":0}
引用次数: 0
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.
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.