{"title":"2型固定高度间隔","authors":"C. Walker, E. Walker","doi":"10.1109/NAFIPS.2007.383902","DOIUrl":null,"url":null,"abstract":"The algebra of truth values for fuzzy sets of type-2, with operations due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting sub algebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about such a sub algebra, one which generalizes the truth value algebra of interval-valued fuzzy sets. We investigate it as an algebra, and determine its automorphism group. In particular, we show that it is a characteristic subalgebra of the containing truth value algebra of fuzzy sets of type-2, and that its automorphisms are exactly those induced by automorphisms of that algebra.","PeriodicalId":292853,"journal":{"name":"NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Type-2 Intervals of Constant Height\",\"authors\":\"C. Walker, E. Walker\",\"doi\":\"10.1109/NAFIPS.2007.383902\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The algebra of truth values for fuzzy sets of type-2, with operations due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting sub algebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about such a sub algebra, one which generalizes the truth value algebra of interval-valued fuzzy sets. We investigate it as an algebra, and determine its automorphism group. In particular, we show that it is a characteristic subalgebra of the containing truth value algebra of fuzzy sets of type-2, and that its automorphisms are exactly those induced by automorphisms of that algebra.\",\"PeriodicalId\":292853,\"journal\":{\"name\":\"NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NAFIPS.2007.383902\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAFIPS.2007.383902","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The algebra of truth values for fuzzy sets of type-2, with operations due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting sub algebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about such a sub algebra, one which generalizes the truth value algebra of interval-valued fuzzy sets. We investigate it as an algebra, and determine its automorphism group. In particular, we show that it is a characteristic subalgebra of the containing truth value algebra of fuzzy sets of type-2, and that its automorphisms are exactly those induced by automorphisms of that algebra.