{"title":"New Grey Relational Analysis for Finding the Invariable Structure and Its Applications","authors":"D. Yamaguchi, GuoDong Li, M. Nagai","doi":"10.30016/JGS.200512.0007","DOIUrl":null,"url":null,"abstract":"Grey relational analysis is a useful method in many fields as well known, and is presented variously, since the distinguish coefficient is fixed on using. This paper proposes a new approach for grey relational analysis that is based on topological background, and this proposal method has 3 features: (1) Grey relational matrix is always symmetric, (2) Order relation of with given samples is followed grey relational grade, (3) Distinguish coefficient is able to find an invariable structure of given data set. Two simulation examples are given, such as IRIS data set and WINE data set. This proposal method is compared with traditional grey relational analysis, about metric calculation and grey relational characteristic. In addition, it has obtained the order of given samples more clearly. And three examples are also given to show how to use the proposal method and distinguish coefficient in pattern recognition, information retrieval, and kansei engineering.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"8 1","pages":"167-178"},"PeriodicalIF":1.0000,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"57","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Grey System","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.30016/JGS.200512.0007","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 57
Abstract
Grey relational analysis is a useful method in many fields as well known, and is presented variously, since the distinguish coefficient is fixed on using. This paper proposes a new approach for grey relational analysis that is based on topological background, and this proposal method has 3 features: (1) Grey relational matrix is always symmetric, (2) Order relation of with given samples is followed grey relational grade, (3) Distinguish coefficient is able to find an invariable structure of given data set. Two simulation examples are given, such as IRIS data set and WINE data set. This proposal method is compared with traditional grey relational analysis, about metric calculation and grey relational characteristic. In addition, it has obtained the order of given samples more clearly. And three examples are also given to show how to use the proposal method and distinguish coefficient in pattern recognition, information retrieval, and kansei engineering.
期刊介绍：
The journal is a forum of the highest professional quality for both scientists and practitioners to exchange ideas and publish new discoveries on a vast array of topics and issues in grey system. It aims to bring forth anything from either innovative to known theories or practical applications in grey system. It provides everyone opportunities to present, criticize, and discuss their findings and ideas with others. A number of areas of particular interest (but not limited) are listed as follows:
Grey mathematics-
Generator of Grey Sequences-
Grey Incidence Analysis Models-
Grey Clustering Evaluation Models-
Grey Prediction Models-
Grey Decision Making Models-
Grey Programming Models-
Grey Input and Output Models-
Grey Control-
Grey Game-
Practical Applications.
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