International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS 2020 2020 NEUTRO-BCK-ALGEBRA Department of Mathematics, University of Payame Noor, Tehran, Iran Mohammad Hamidi Mathematics & Science, University of New Mexico, Gallup Campus, USA Florentin Smarandache 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. 2020 2020 110 117 10.54216/IJNS.080204