{"title":"基于结构元法的模糊数的比较与排序","authors":"Si-zong GUO","doi":"10.1016/S1874-8651(10)60013-0","DOIUrl":null,"url":null,"abstract":"<div><p>According to the homeomorphic property between fuzzy number space and the family of standard monotone functions on [−1,1], comparison of fuzzy numbers can be transformed into comparison of standard monotone functions on [−1,1]. Some order relations on the fuzzy number space are defined by using the method of fuzzy structured element, and some properties of the order relations are discussed. At last, an example is designed.</p></div>","PeriodicalId":101206,"journal":{"name":"Systems Engineering - Theory & Practice","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1874-8651(10)60013-0","citationCount":"12","resultStr":"{\"title\":\"Comparison and Ordering of Fuzzy Numbers Based on Method of Structured Element\",\"authors\":\"Si-zong GUO\",\"doi\":\"10.1016/S1874-8651(10)60013-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>According to the homeomorphic property between fuzzy number space and the family of standard monotone functions on [−1,1], comparison of fuzzy numbers can be transformed into comparison of standard monotone functions on [−1,1]. Some order relations on the fuzzy number space are defined by using the method of fuzzy structured element, and some properties of the order relations are discussed. At last, an example is designed.</p></div>\",\"PeriodicalId\":101206,\"journal\":{\"name\":\"Systems Engineering - Theory & Practice\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1874-8651(10)60013-0\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems Engineering - Theory & Practice\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1874865110600130\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems Engineering - Theory & Practice","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1874865110600130","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Comparison and Ordering of Fuzzy Numbers Based on Method of Structured Element
According to the homeomorphic property between fuzzy number space and the family of standard monotone functions on [−1,1], comparison of fuzzy numbers can be transformed into comparison of standard monotone functions on [−1,1]. Some order relations on the fuzzy number space are defined by using the method of fuzzy structured element, and some properties of the order relations are discussed. At last, an example is designed.
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