Fuzzy Ideals of Sheffer Stroke Hilbert Algebras

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2022-07-30 DOI:10.1007/s40010-022-00794-9
Tahsin Oner, Tugce Katican, Arsham Borumand Saeid
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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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Sheffer Stroke Hilbert代数的模糊理想
本文讨论了Sheffer冲程Hilbert代数上的模糊子代数及其t-适形理想。我们陈述并证明了具有T形T的模糊子代数(简称T-模糊子代数)的水平集与Sheffer冲程Hilbert代数的子代数之间的关系。然后分析了t -模糊子代数的组成和Sheffer冲程Hilbert代数的同态。通过定义Sheffer冲程Hilbert代数的模糊子代数,研究了该代数结构的模糊子代数与t -模糊子代数之间的关系。此外,还证明了每一个与T符合的模糊理想(简而言之,T-模糊理想)都是一个T-模糊子代数,但反之并不普遍成立。与Sheffer冲程Hilbert代数的T-fuzzy子代数一样,证明了T-fuzzy理想的一些性质。
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来源期刊
CiteScore
2.60
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology
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