Soft Subalgebras and Ideals of Sheffer Stroke Hilbert Algebras based on $\mathcal{N}$-Structures

In this study, we introduce the concepts of $\mathcal{N}$-ideals of types $(\in, \in)$ and $(\in, \in \vee \kq)$, along with soft $\mathcal{N}_\in$-sets, soft $\mathcal{N}_\kq$-sets, and soft $\mathcal{N}_{\in \vee \kq}$-sets. Additionally, we define soft $\mathcal{N}$-subalgebras and $\mathcal{N}$-ideals within the context of Sheffer stroke Hilbert algebras and explore various properties of these structures. The paper also provides characterizations of $\mathcal{N}$-subalgebras of types $(\in, \in)$ and $(\in, \in \vee \kq)$, as well as $\mathcal{N}$-ideals for both of these types. Furthermore, we further examine their corresponding soft versions, extending the algebraic framework in the setting of Sheffer stroke Hilbert algebras.