{"title":"模糊系统的帧逼近- siso情况","authors":"A. Shmilovici, O. Maimon","doi":"10.1109/FUZZY.1995.409961","DOIUrl":null,"url":null,"abstract":"In this paper, the approximation problem of SISO fuzzy systems by frames is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basis functions (FBF), we first discuss the mathematical theory of frames in a Hilbert space, and then the conditions under which a FBF is a valid frame. Fuzzy membership functions which constitute a valid frame can universally approximate any continuous function. The triangular membership function is demonstrated as such, and it's approximation properties are discussed.<<ETX>>","PeriodicalId":150477,"journal":{"name":"Proceedings of 1995 IEEE International Conference on Fuzzy Systems.","volume":"320 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Fuzzy systems approximation by frames-SISO case\",\"authors\":\"A. Shmilovici, O. Maimon\",\"doi\":\"10.1109/FUZZY.1995.409961\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the approximation problem of SISO fuzzy systems by frames is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basis functions (FBF), we first discuss the mathematical theory of frames in a Hilbert space, and then the conditions under which a FBF is a valid frame. Fuzzy membership functions which constitute a valid frame can universally approximate any continuous function. The triangular membership function is demonstrated as such, and it's approximation properties are discussed.<<ETX>>\",\"PeriodicalId\":150477,\"journal\":{\"name\":\"Proceedings of 1995 IEEE International Conference on Fuzzy Systems.\",\"volume\":\"320 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1995 IEEE International Conference on Fuzzy Systems.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FUZZY.1995.409961\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 1995 IEEE International Conference on Fuzzy Systems.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.1995.409961","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, the approximation problem of SISO fuzzy systems by frames is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basis functions (FBF), we first discuss the mathematical theory of frames in a Hilbert space, and then the conditions under which a FBF is a valid frame. Fuzzy membership functions which constitute a valid frame can universally approximate any continuous function. The triangular membership function is demonstrated as such, and it's approximation properties are discussed.<>
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