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Submitted
February 12, 2022
Accepted
February 1, 2023
Published
March 30, 2023
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Abstract

In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N −subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals.

Keywords

Sheffer stroke BCK-algebra subalgebra ideal neutrosophic N − subalgebra neutrosophic N −ideal

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How to Cite
Oner, T., Katican, T., & Rezaei, A. (2023). Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras. Journal of the Indonesian Mathematical Society, 29(1), 45–63. https://doi.org/10.22342/jims.29.1.1165.45-63
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References

  1. Abbott, J. C., Implicational Algebras, Bulletin Math´ematique de la Soci´et´e des Sciences Math´ematiques de la R´epublique Socialiste de Roumanie, 11(1) (1967), 3-23.
  2. Atanassov, K. T., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
  3. Chajda, I., Sheffer Operation in Ortholattices, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium. Mathematica, 44(1) (2005), 19-23.
  4. Imai, Y. and Is´eki, K., On Axiom Systems of Proposional Calculi, XIV. Proc. Jpn. Acad., Ser. A, Math. Sci., 42 (1966), 1922.
  5. Jun, Y. B., Lee, K. J. and Song, S. Z., N −ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc., 22 (2009), 417-437.
  6. Jun, Y. B., Smarandache, F. and Bordbar, H., Neutrosophic N−structures applied to BCK/BCI-algebras, Information, 8(128) (2017), 1-12.
  7. Katican, T., Oner, T., Rezaei, A. and Smarandache, F., Neutrosophic N-structures Applied to Sheffer Stroke BL-Algebras, CMES-Computer Modeling in Engineering & Sciences, 129(1) (2021), 355-372.
  8. Khan, M., Anis, S., Smarandache, F. and Jun, Y. B., Neutrosophic N −structures and their applications in semigroups, Infinite Study, (2017).
  9. McCune, W., Veroff, R., Fitelson, B., Harris, K., Feist, A. and Wos, L., Short Single axioms for Boolean algebra, Journal of Automated Reasoning, 29(1) (2002), 1-16.
  10. Oner, T., Katican, T. and Rezaei, A., Neutrosophic N-structures on strong Sheffer stroke non-associative MV-algebras, Neutrosophic Sets and Systems, 40 (2021), 235-252.
  11. Oner, T., Katican, T. and Borumand Saeid, A., Neutrosophic N-structures on Sheffer stroke Hilbert algebras, Neutrosophic Sets and Systems, 42 (2021), 221-238.
  12. Oner, T., Katican, T. and Borumand Saeid, A., Hesitant fuzzy structures on Sheffer stroke BCK-algebras, New Mathematics and Natural Computation, (2023), 1-12.
  13. Oner, T., Kalkan, T., Katican, T. and Rezaei, A., Fuzzy implivative ideals of Sheffer stroke BG-algebras, Facta Universitatis Series Mathematics and Informatics, 36(4) (2021), 913-926.
  14. Oner, T., Kalkan, T. and Borumand Saeid, A., Class of Sheffer Stroke BCK-Algebras, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 30(1) (2022), 247-269.
  15. Sheffer, H. M., A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4) (1913), 481-488.
  16. Smarandache, F., A unifying field in logic. Neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, NM, USA, 1999.
  17. Smarandache, F., Neutrosophic set-A generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287-297.
  18. Song, S. Z., Smarandache, F. and Jun, Y. B., Neutrosophic Commutative N −ideals in BCK-algebras, Information, 8(130) (2017).
  19. Zadeh, L. A., Fuzzy sets, Inf. Control, 8 (1965), 338-353