{"title":"多标准决策的锥形排序","authors":"Andreas H Hamel, Daniel Kostner","doi":"arxiv-2312.03006","DOIUrl":null,"url":null,"abstract":"Recently introduced cone distribution functions from statistics are turned\ninto multi-criteria decision making (MCDM) tools. It is demonstrated that this\nprocedure can be considered as an upgrade of the weighted sum scalarization\ninsofar as it absorbs a whole collection of weighted sum scalarizations at once\ninstead of fixing a particular one in advance. Moreover, situations are\ncharacterized in which different types of rank reversal occur, and it is\nexplained why this might even be useful for analyzing the ranking procedure. A\nfew examples will be discussed and a potential application in machine learning\nis outlined.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"485 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cone Ranking for Multi-Criteria Decision Making\",\"authors\":\"Andreas H Hamel, Daniel Kostner\",\"doi\":\"arxiv-2312.03006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently introduced cone distribution functions from statistics are turned\\ninto multi-criteria decision making (MCDM) tools. It is demonstrated that this\\nprocedure can be considered as an upgrade of the weighted sum scalarization\\ninsofar as it absorbs a whole collection of weighted sum scalarizations at once\\ninstead of fixing a particular one in advance. Moreover, situations are\\ncharacterized in which different types of rank reversal occur, and it is\\nexplained why this might even be useful for analyzing the ranking procedure. A\\nfew examples will be discussed and a potential application in machine learning\\nis outlined.\",\"PeriodicalId\":501330,\"journal\":{\"name\":\"arXiv - MATH - Statistics Theory\",\"volume\":\"485 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2312.03006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.03006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Recently introduced cone distribution functions from statistics are turned
into multi-criteria decision making (MCDM) tools. It is demonstrated that this
procedure can be considered as an upgrade of the weighted sum scalarization
insofar as it absorbs a whole collection of weighted sum scalarizations at once
instead of fixing a particular one in advance. Moreover, situations are
characterized in which different types of rank reversal occur, and it is
explained why this might even be useful for analyzing the ranking procedure. A
few examples will be discussed and a potential application in machine learning
is outlined.
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