{"title":"Optimal function approximation using fuzzy rules","authors":"D. Lisin, M. Gennert","doi":"10.1109/NAFIPS.1999.781679","DOIUrl":null,"url":null,"abstract":"It has been constructively proven by Kosko (1994) that fuzzy systems are universal approximators. However, the proof does not provide an algorithm to build a fuzzy system that approximates an analytically defined function to an arbitrary precision with a minimum number of fuzzy rules. We describe a method that utilizes the information contained in the analytic definition of a function, such as its first and second derivatives, to build a fuzzy system that approximates it.","PeriodicalId":335957,"journal":{"name":"18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAFIPS.1999.781679","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
It has been constructively proven by Kosko (1994) that fuzzy systems are universal approximators. However, the proof does not provide an algorithm to build a fuzzy system that approximates an analytically defined function to an arbitrary precision with a minimum number of fuzzy rules. We describe a method that utilizes the information contained in the analytic definition of a function, such as its first and second derivatives, to build a fuzzy system that approximates it.