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Neutrosophic N-Structures Applied to Sheffer Stroke BL-Algebras

Tugce Katican1, Tahsin Oner1, Akbar Rezaei2,*, 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 this 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.

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


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.


Sheffer stroke BL-algebra; (ultra) filter; neutrosophic N-subalgebra; (ultra) neutrosophic N-filter

Cite This Article

Katican, T., Oner, T., Rezaei, A., Smarandache, F. (2021). Neutrosophic -Structures Applied to Sheffer Stroke BL-Algebras. CMES-Computer Modeling in Engineering & Sciences, 129(1), 355–372.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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