{"title":"Fuzzy Ideals of Sheffer Stroke Hilbert Algebras","authors":"Tahsin Oner, Tugce Katican, Arsham Borumand Saeid","doi":"10.1007/s40010-022-00794-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm <i>T</i> (briefly, <i>T</i>-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of <i>T</i>-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and <i>T</i>-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm <i>T</i> (in short, <i>T</i>-fuzzy ideal) is a <i>T</i>-fuzzy subalgebra but the converse does not generally hold. As in <i>T</i>-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the <i>T</i>-fuzzy ideals are proved.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-022-00794-9","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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Abstract
In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T (briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and T-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm T (in short, T-fuzzy ideal) is a T-fuzzy subalgebra but the converse does not generally hold. As in T-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the T-fuzzy ideals are proved.
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