In this paper, we have defined rough statistical convergence in intuitionistic fuzzy normed spaces which is an useful characterization in the field of statistical convergence. We have proved some properties related to rough convergence which provides some new functional tools in the situation of uncertainty like intuitionistic fuzzy normed spaces. Further, we have established the relationship between the set of statistical limit points and set of cluster points of rough statistically convergent sequences in these spaces.

In the present paper, the basic objective of our work is to define Δᵐ-statistical convergence in the setup of intuitionistic fuzzy normed spaces for double sequences. We have proved some examples which shows this method of convergence is more generalized. Further, we defined the Δᵐ-statistical Cauchy sequences in these spaces and given the Cauchy convergence criterion for this new notion of convergence.

The main purpose of this work is to define Rough Statistical \(\Lambda\)-Convergence of order \(\alpha\) \((0<\alpha\leq1)\) in normed linear spaces. We have proved some basic properties and also provided some examples to show that this method of convergence is more generalized than the rough statistical convergence. Further, we have shown the results related to statistically \(\Lambda\)-bounded sets of order \(\alpha\) and sets of rough statistically \(\Lambda\)-convergent sequences of order \(\alpha\).

The basic purpose of our work is to define $\lambda$-statistical convergence for the generalized difference sequences (i.e. \(\lambda\)-\(\Delta^m\)-statistical convergence) on Intuitionistic Fuzzy Normed space (IFN space). We have proven topological results about this generalized method of sequence convergence. Also, we have given the \(\lambda\)-\(\Delta^m\)-statistical Cauchy sequences along with its Cauchy criteria of convergence on these spaces.

The purpose of the present article is to introduce the idea of rough ideal statistical convergence of order $\alpha$ of sequences in intuitionistic fuzzy normed spaces. In these spaces, we have defined the concepts of rough ideal statistical limit points, rough ideal cluster points, and rough ideal boundedness. The theory of convexity and closeness was next examined for the collection of approximative statistical limit points.