On some topological properties of intuitionistic $2$-fuzzy $n$-normed linear spaces

Abstract

Motivated by the notion of $n$-norm due to Gähler, in this article we define the concept of intuitionistic $2$-fuzzy $n$-normed space in general setting of $t$-norm as a generalization of intuitionistic fuzzy normed space in the sense of Bag and Samanta. Further we define the notion of $\alpha$-$n$-norm corresponding to intuitionistic $2$-fuzzy $n$-norm. In addition, we discuss some basic properties of convergence and completeness for intuitionistic $2$-fuzzy $n$-normed spaces.