{"title":"用泛函分析的概念研究近似推理和模糊控制","authors":"H. Thiele","doi":"10.1109/KES.1997.619428","DOIUrl":null,"url":null,"abstract":"We investigate the input-output behaviour of the inference machine of a fuzzy controller, which is interpreted as a functional operator operating on the set of all fuzzy sets defined on a given universe. The concepts of fixed point, eigen function, eigen value and linearity are suitably translated into the fuzzy approach presented. Classical fixed point theorems (Birkhoff, Zorn, Banach) are applied in order to investigate the behaviour of inference machines. The concept of linearity is studied for Mamdani interpretations.","PeriodicalId":166931,"journal":{"name":"Proceedings of 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97","volume":"129 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Investigating approximate reasoning and fuzzy control by concepts of functional analysis\",\"authors\":\"H. Thiele\",\"doi\":\"10.1109/KES.1997.619428\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the input-output behaviour of the inference machine of a fuzzy controller, which is interpreted as a functional operator operating on the set of all fuzzy sets defined on a given universe. The concepts of fixed point, eigen function, eigen value and linearity are suitably translated into the fuzzy approach presented. Classical fixed point theorems (Birkhoff, Zorn, Banach) are applied in order to investigate the behaviour of inference machines. The concept of linearity is studied for Mamdani interpretations.\",\"PeriodicalId\":166931,\"journal\":{\"name\":\"Proceedings of 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97\",\"volume\":\"129 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/KES.1997.619428\",\"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 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/KES.1997.619428","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Investigating approximate reasoning and fuzzy control by concepts of functional analysis
We investigate the input-output behaviour of the inference machine of a fuzzy controller, which is interpreted as a functional operator operating on the set of all fuzzy sets defined on a given universe. The concepts of fixed point, eigen function, eigen value and linearity are suitably translated into the fuzzy approach presented. Classical fixed point theorems (Birkhoff, Zorn, Banach) are applied in order to investigate the behaviour of inference machines. The concept of linearity is studied for Mamdani interpretations.
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