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.

Keywords

• intuitionistic fuzzy set,fuzzy set,$2$-fuzzy $n$-normed space,$t$-norm,$t$-conorm

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