{"title":"The Essential of GM(1,1) Model","authors":"Xiaoxuan Zhang","doi":"10.30016/JGS.200709.0004","DOIUrl":null,"url":null,"abstract":"This paper reveals that GM(1,1) model is actually constructed according to the first order linearly differential equation, it is an equation that exponential sequences satisfy, so the essential of GM(1,1) model is an exponential sequence model. Though GM(1,1) model is constructed according to the first order linearly differential equation, both are not the same, this paper shows their features in common and differences. In addition, this paper proposes that models constructed according to the first order linearly differential equation are not unique, the author constructs another exponential sequence model, we might as well call it grey exponential model(GEM), it can replace GM(1,1) model for predicting of grey systems.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"81-87"},"PeriodicalIF":1.0000,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Grey System","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.30016/JGS.200709.0004","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: 1
Abstract
This paper reveals that GM(1,1) model is actually constructed according to the first order linearly differential equation, it is an equation that exponential sequences satisfy, so the essential of GM(1,1) model is an exponential sequence model. Though GM(1,1) model is constructed according to the first order linearly differential equation, both are not the same, this paper shows their features in common and differences. In addition, this paper proposes that models constructed according to the first order linearly differential equation are not unique, the author constructs another exponential sequence model, we might as well call it grey exponential model(GEM), it can replace GM(1,1) model for predicting of grey systems.
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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