{"title":"模糊逻辑函数的范式","authors":"I. Perfilieva","doi":"10.1109/ISMVL.2003.1201385","DOIUrl":null,"url":null,"abstract":"Three types of normal forms are introduced for fuzzy logic functions: disjunctive, conjunctive and additive. Disjunctive and conjunctive normal forms are considered in two variants: infinite and finite. It is shown that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any L-valued function where L is a support set of any complete BL-algebra. The additive normal form \"lies\" in the middle of the two others. For all of them the estimation of the quality of approximation is suggested.","PeriodicalId":434515,"journal":{"name":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Normal forms for fuzzy logic functions\",\"authors\":\"I. Perfilieva\",\"doi\":\"10.1109/ISMVL.2003.1201385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Three types of normal forms are introduced for fuzzy logic functions: disjunctive, conjunctive and additive. Disjunctive and conjunctive normal forms are considered in two variants: infinite and finite. It is shown that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any L-valued function where L is a support set of any complete BL-algebra. The additive normal form \\\"lies\\\" in the middle of the two others. For all of them the estimation of the quality of approximation is suggested.\",\"PeriodicalId\":434515,\"journal\":{\"name\":\"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2003.1201385\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2003.1201385","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Three types of normal forms are introduced for fuzzy logic functions: disjunctive, conjunctive and additive. Disjunctive and conjunctive normal forms are considered in two variants: infinite and finite. It is shown that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any L-valued function where L is a support set of any complete BL-algebra. The additive normal form "lies" in the middle of the two others. For all of them the estimation of the quality of approximation is suggested.
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