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ARTICLE

Neutrosophic N-Structures Applied to Sheffer Stroke BL-Algebras

Tugce Katican¹, Tahsin Oner¹, Akbar Rezaei^2,*, Florentin Smarandache³

1 Department of Mathematics, Ege University, Izmir, 35100, Turkey
2 Department of Mathematics, Payame Noor University, Tehran, 19395-4697, Iran
3 Department of Mathematics and Science, University of New Mexico, Gallup, 87301, NM, USA

* Corresponding Author: Akbar Rezaei. Email:

(This article belongs to the Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2021, 129(1), 355-372. https://doi.org/10.32604/cmes.2021.016996

Received 18 April 2021; Accepted 25 May 2021; Issue published 24 August 2021

Abstract

In this paper, we introduce a neutrosophic N-subalgebra, a (ultra) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties on a Sheffer stroke BL-algebra. By defining a quasi-subalgebra of a Sheffer stroke BL-algebra, it is proved that the level set of neutrosophic N-subalgebras on the algebraic structure is its quasi-subalgebra and vice versa. Then we show that the family of all neutrosophic N-subalgebras of a Sheffer stroke BL-algebra forms a complete distributive lattice. After that a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is described, we demonstrate that every neutrosophic N-filter of a Sheffer stroke BL-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. Finally, it is presented that a level set of a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is also its (ultra) filter and the inverse is always true. Moreover, some features of neutrosophic N-structures on a Sheffer stroke BL-algebra are investigated.

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Keywords

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