A Generalization of Subnexuses Based on $\mathcal{N}$-Structures

Morteza Norouzi, Ameneh Asadi, Young Bae Jun

Abstract

In this paper, we generalize the concepts of ${\mathcal{N}}$-subnexuses of types $(\in, q)$, $(\in, \in \vee{q})$ and $(q, \in \vee {q})$, and introduce the notions of ${\mathcal{N}}$-subnexuses of types $(\in, q_{k})$, $(\in, \in \vee{q_{k}})$ and $(q, \in \vee {q_{k}})$. We investigate their basicproperties, characterize subnexuses by ${\mathcal{N}}$-subnexuses of type $(\in, \in \vee {q_{k}})$, and give some characterizations for${\mathcal{N}}$-subnexuses of types $(\in, q_{k})$ and $(q, \in \vee{q_{k}})$. Moreover, we define ${\mathcal{N}}$-subnexuses of type $(\overline{\in}, \overline{\in} \vee \overline{q_{k}})$ and discusson their different properties.