1 Affiliation : Department of Mathematics, University of Payame Noor, Tehran, Iran
Email : firstname.lastname@example.org
2 Affiliation : Mathematics & Science, University of New Mexico, Gallup Campus, USA
Email : email@example.com
This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK algebra and shows that Neutro-BCK-algebra are different from BCKalgebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hassdiagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.
Neutro-BCK-algebra , NeutroPoset , Neutro-Hass diagram.
 M. Al-Tahan, Neutrosophic N -Ideals (N -Subalgebras) of Subtraction Algebra. International Journal ofNeutrosophic Science, 3, no.1, pp.44-53,2020.
 Y. Imai and K. Iseki, On axioms systems of propositional calculi , XIV, Proc. Japan Academy, 42, pp.19-22,1966.
 T. Jech, Set Theory , The 3rd Millennium Edition, Springer Monographs in Mathematics, 2002.
 A. Rezaei, F. Smarandache, The Neutrosophic Triplet of BI-algebras, Neutrosophic Sets and Systems, 33, pp. 313-321, 2020.
 A. Rezaei, F. Smarandache, On Neutro-BE-algebras and Anti-BE-algebras,International Journal of Neutrosophic Science, 4, no. 1, pp. 08–15,2020
 F. Smarandache, A. Rezaei, H.S. Kim, A new trend to extensions of CI-algebras,International Journal ofNeutrosophic Science, 5 , no.1, pp. 8–15,2020.
 F. Smarandache, Neutro algebra is a generalization of partial algebra,International Journal of Neutrosophic Science, 2 , no.1, pp.8-17,