{"title":"有界Heyting代数中的模糊交换理想和隐含理想","authors":"Chunhui Liu","doi":"10.1109/ICSAI57119.2022.10005393","DOIUrl":null,"url":null,"abstract":"In this paper, the problem of ideals is studied in bounded Heyting algebras by using the principle and method of fuzzy sets theory. The notions of fuzzy commutative and implicative ideals are introduced in bounded Heyting algebras and some of their properties and relations are investigated. Some equivalent characterizations are obtained of fuzzy commutative and fuzzy implicative ideals. At the same time, a necessary and sufficient condition for a fuzzy commutative ideal forms a fuzzy implicative ideal is proved.","PeriodicalId":339547,"journal":{"name":"2022 8th International Conference on Systems and Informatics (ICSAI)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Fuzzy Commutative and Implicative ideals in Bounded Heyting Algebras\",\"authors\":\"Chunhui Liu\",\"doi\":\"10.1109/ICSAI57119.2022.10005393\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the problem of ideals is studied in bounded Heyting algebras by using the principle and method of fuzzy sets theory. The notions of fuzzy commutative and implicative ideals are introduced in bounded Heyting algebras and some of their properties and relations are investigated. Some equivalent characterizations are obtained of fuzzy commutative and fuzzy implicative ideals. At the same time, a necessary and sufficient condition for a fuzzy commutative ideal forms a fuzzy implicative ideal is proved.\",\"PeriodicalId\":339547,\"journal\":{\"name\":\"2022 8th International Conference on Systems and Informatics (ICSAI)\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 8th International Conference on Systems and Informatics (ICSAI)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICSAI57119.2022.10005393\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 8th International Conference on Systems and Informatics (ICSAI)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICSAI57119.2022.10005393","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fuzzy Commutative and Implicative ideals in Bounded Heyting Algebras
In this paper, the problem of ideals is studied in bounded Heyting algebras by using the principle and method of fuzzy sets theory. The notions of fuzzy commutative and implicative ideals are introduced in bounded Heyting algebras and some of their properties and relations are investigated. Some equivalent characterizations are obtained of fuzzy commutative and fuzzy implicative ideals. At the same time, a necessary and sufficient condition for a fuzzy commutative ideal forms a fuzzy implicative ideal is proved.
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