{"title":"区间型-2布尔模糊系统是普遍逼近器","authors":"F. You, H. Ying","doi":"10.1109/NAFIPS.2010.5548180","DOIUrl":null,"url":null,"abstract":"Unlike the Mamdani and TS fuzzy systems, a Boolean fuzzy system, type-1 or type-2, employs a fuzzy implication to interpret its rules. There exist three families of type-2 fuzzy implications – R-implication, S-implication and QL-implication. In this paper, using the same technique that we developed previously [22, 23], we constructively prove that all the interval type-2 Boolean fuzzy systems, regardless of the implication they use, are universal approximators in that they are capable of uniformly approximating any real multivariate continuous function on a compact domain to any degree of accuracy.","PeriodicalId":394892,"journal":{"name":"2010 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Interval type-2 Boolean fuzzy systems are universal approximators\",\"authors\":\"F. You, H. Ying\",\"doi\":\"10.1109/NAFIPS.2010.5548180\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Unlike the Mamdani and TS fuzzy systems, a Boolean fuzzy system, type-1 or type-2, employs a fuzzy implication to interpret its rules. There exist three families of type-2 fuzzy implications – R-implication, S-implication and QL-implication. In this paper, using the same technique that we developed previously [22, 23], we constructively prove that all the interval type-2 Boolean fuzzy systems, regardless of the implication they use, are universal approximators in that they are capable of uniformly approximating any real multivariate continuous function on a compact domain to any degree of accuracy.\",\"PeriodicalId\":394892,\"journal\":{\"name\":\"2010 Annual Meeting of the North American Fuzzy Information Processing Society\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Annual Meeting of the North American Fuzzy Information Processing Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NAFIPS.2010.5548180\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Annual Meeting of the North American Fuzzy Information Processing Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAFIPS.2010.5548180","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interval type-2 Boolean fuzzy systems are universal approximators
Unlike the Mamdani and TS fuzzy systems, a Boolean fuzzy system, type-1 or type-2, employs a fuzzy implication to interpret its rules. There exist three families of type-2 fuzzy implications – R-implication, S-implication and QL-implication. In this paper, using the same technique that we developed previously [22, 23], we constructively prove that all the interval type-2 Boolean fuzzy systems, regardless of the implication they use, are universal approximators in that they are capable of uniformly approximating any real multivariate continuous function on a compact domain to any degree of accuracy.
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