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 this work we define $(\lambda, \mu)-$statistical summability and $(V, \lambda, \mu)-$\\summability of order $\tilde{\alpha}$ for double sequences and obtain some relations between these summability methods. We demonstrate examples which shows our method of summability is more general for double sequences.

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 main objective of work is to study the concept of rough I-statistical convergence for Copson-transformation in the setup of neutrosophic normed spaces by considering algebraic and topological properties of the set of rough ideal statistical limit points for Copson transformation sequences. We also defined the set of rough I-statistical cluster points and investigated some properties for the sequences using Copson-transformation.