SB-neutrosophic structures in BCK/BCI-algebras

This article presents the novel set termed SB-neutrosophic set (SB-NSS), which extends the concept of the Neutrosophic set (NSS). We illustrate its fundamental operations with examples. This concept of SB-NSSs is applied to BCK/BCI-algebras, and we introduce the notion of SB-neutrosophic subalgebra (SB-NSSA), SB-neutrosophic ideal (SB-NSI), and related properties are investigated. Furthermore, we provide conditions for an SB-NSS to be an SB-NSSA, for an SB-NSS to be an SB-NSI, and for an SB-NSSA to be an SB-NSI. In a BCI-algebra, conditions for an SB-NSI to be an SB-NSSA are given.