ech T Press Science Computer Modeling in Engineering & Sciences DOI: 10.32604/cmes.2021.016996 ARTICLE Neutrosophic N -Structures Applied to Shefer Stroke BL-Algebras Tugce Katican 1 , Tahsin Oner 1 , Akbar Rezaei 2,* and Florentin Smarandache 3 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: rezaei@pnu.ac.ir Received: 18 April 2021 Accepted: 25 May 2021 ABSTRACT In this paper, we introduce a neutrosophic N -subalgebra, a (ultra) neutrosophic N -flter, level sets of these neutrosophic N -structures and their properties on a Shefer stroke BL-algebra. By defning a quasi-subalgebra of a Shefer 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 Shefer stroke BL-algebra forms a complete distributive lattice. Afer that a (ultra) neutrosophic N -flter of a Shefer stroke BL-algebra is described, we demonstrate that every neutrosophic N -flter of a Shefer 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 -flter of a Shefer stroke BL-algebra is also its (ultra) flter and the inverse is always true. Moreover, some features of neutrosophic N -structures on a Shefer stroke BL-algebra are investigated. KEYWORDS Shefer stroke BL-algebra; (ultra) flter; neutrosophic N -subalgebra; (ultra) neutrosophic N -flter 1 Introduction Fuzzy set theory, which has the truth (t) (membership) function and state positive meaning of information, is introduced by Zadeh [1] as a generalization the classical set theory. This led scien- tists to fnd negative meaning of information. Hence, intuitionistic fuzzy sets [2] which are fuzzy sets with the falsehood (f) (nonmembership) function were introduced by Atanassov. However, there exist uncertainty and vagueness in the language, as well as positive ana negative meaning of information. Thus, Smarandache defned neutrosophic sets which are intuitionistic fuzzy sets with the indeterminacy/neutrality (i) function [3,4]. Thereby, neutrosophic sets are determined on three components: (t, i, f ) : (truth, indeterminacy, falsehood ) [5]. Since neutrosophy enables that information in language can be comprehensively examined at all points, many researchers applied neutrosophy to different theoretical areas such as BCK/BCI-algebras, BE-algebras, semigroups, metric spaces, Sheffer stroke Hilbert algebras and strong Sheffer stroke non-associative MV- algebras [6–15] so as to improve devices imitating human behaviours and thoughts, artifcial intelligence and technological tools. This work is licensed under a Creative Commons Attribution 4.0 International License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.