A Note on Generalized Intuitionistic Fuzzy $\psi$ Normed Linear Space

TL;DR

This paper introduces a generalized intuitionistic fuzzy $\psi$ norm in linear spaces, develops related properties, and proves the equivalence of different notions of continuity within this framework.

Contribution

It defines the generalized intuitionistic fuzzy $\psi$ norm and explores its properties, including continuity concepts, in linear spaces for the first time.

Findings

Development of generalized intuitionistic fuzzy $\psi$ norm

Establishment of properties of fuzzy $\psi$ normed linear spaces

Equivalence of different continuity notions in this context

Abstract

In respect of the definition of intuitionistic fuzzy n-norm \cite{Vijayabalaji}, the definition of generalised intuitionistic fuzzy $\psi$ norm (\, in short GIF$\psi$N \,) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy $\psi$ normed linear space and finite dimensional generalized intuitionistic fuzzy $\psi$ normed linear space have been developed. Lastly, we have introduced the definitions of generalised intuitionistic fuzzy $\psi$ continuity , sequentially intuitionistic fuzzy $\psi$ continuity and it is proved that they are equivalent.