Neutrosophic N--structures on Sheffer stroke BCH-algebras

The aim of the study is to introduce a neutrosophic N--subalgebra and neutrosophic N--ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N--subalgebra (neutrosophic N--ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown...

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Published inNeutrosophic sets and systems Vol. 50; pp. 459 - 479
Main Authors Oner, Tahsin, Katican, Tugce, Rezaei, Akbar
Format Journal Article
LanguageEnglish
Published Neutrosophic Sets and Systems 01.09.2022
University of New Mexico
Subjects
Algebra
neutrosophic n-ideal
neutrosophic n-subalgebra
sheffer stroke bch-algebra
subalgebra
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Summary:The aim of the study is to introduce a neutrosophic N--subalgebra and neutrosophic N--ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N--subalgebra (neutrosophic N--ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N--subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N--ideal of a Sheffer stroke BCH-algebra is its neutrosophic N--subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N--ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N--functions on this algebraic structure and some properties are investigated. Keywords: Sheffer stroke BCH-algebra; subalgebra; neutrosophic N-- subalgebra; neutrosophic N--ideal.
ISSN:2331-6055
2331-608X
DOI:10.5281/zenodo.6774885