{"title":"关于bl -代数及其区间对应物","authors":"R. Paiva, R. Santiago, B. Bedregal","doi":"10.5540/TEMA.2019.020.02.241","DOIUrl":null,"url":null,"abstract":"Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.","PeriodicalId":163536,"journal":{"name":"TEMA - Tendências em Matemática Aplicada e Computacional","volume":"502 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On BL-Algebras and its Interval Counterpart\",\"authors\":\"R. Paiva, R. Santiago, B. Bedregal\",\"doi\":\"10.5540/TEMA.2019.020.02.241\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.\",\"PeriodicalId\":163536,\"journal\":{\"name\":\"TEMA - Tendências em Matemática Aplicada e Computacional\",\"volume\":\"502 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"TEMA - Tendências em Matemática Aplicada e Computacional\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5540/TEMA.2019.020.02.241\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"TEMA - Tendências em Matemática Aplicada e Computacional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5540/TEMA.2019.020.02.241","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.
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