In this paper, we define strong deferred summability and deferred statistical summability in Intuitionistic fuzzy \(n\)-normed linear spaces (briefly called IF-\(n\)-NLS) and study some of their properties. We also define deferred statistical Cauchy sequence deferred statistical completeness and characterize deferred statistical summability in such spaces. Finally, we will compare deferred statistical summability for different pairs of sequences $\alpha(\ell)$, $\gamma(\ell)$,$u(\ell)$ and $v(\ell)$ satisfying $\alpha(\ell) \leq u(\ell) < v(\ell) \leq \gamma(\ell)$.

The object of this paper is to introduce the notion of Intuitionistic fuzzy continuous mappings and Intuitionistic fuzzy bounded linear operators from one Intuitionistic fuzzy n-normed linear space to another. Relation between Intuitionistic fuzzy continuity and Intuitionistic fuzzy bounded linear operators are studied and some interesting results are obtained.

The aim of this paper is to present the new and interesting notion of ascending family of a- n-norms corresponding to an Intuitionistic fuzzy nnormed linear space. The notion of best aproximation sets in an a- n-normed space corresponding to an Intuitionistic fuzzy n-normed linear space is also defined and several related results are obtained.

In this paper, focus is on the study of spectrum and the spectral properties of bounded linear operators in Intuitionistic fuzzy pseudo normed linear spaces(IFPNLS). It is done by studying regular value, resolvent set, spectrum of a linear operator in IFPNLS. Also, some properties of spectrum and resolvent of strongly Intuitionistic fuzzy bounded(IFB) linear operators in IFPNLS are being developed. It is observed that, for a linear operator $P$ in an IFPNLS, the resolvent set $\rho(P)$ and spectrum $\sigma(P)$ are nonempty, $\rho(P)$ is open and $\sigma(P)$ is closed set.

In order to create a dynamic measure that describes distances between spatiotemporal points whose positions change over time as well as between the data represented by these points, a temporal Intuitionistic fuzzy metric space is created in this paper. The notions of temporal fuzzy t-norm, temporal fuzzy tconorm, and temporal fuzzy negation which have not previously been discussed in the literature are defined, and some of their fundamental characteristics are investigated, in order to define this new method. The idea that the degrees of nearness and non-nearness change with time is the basis for a novel definition of the concept of temporal Intuitionistic fuzzy metric spaces. However, the basic topological characteristics of the temporal Intuitionistic fuzzy metric space are also looked at. We demonstrate how this new temporal metric space preserves the basic characteristics offered by both classical and fuzzy metric spaces. As a result, a new, more flexible, and dynamic metric topology is created while maintaining the fundamental topological characteristics of fuzzy and Intuitionistic fuzzy metric spaces.

The purpose of this article is to introduce the triple sequences and its convergence over instuitionistic fuzzy metric space (IFMS). The article also discusses ideal convergence of triple sequences, the uniqueness of ideal limits, the relationship between Pringsheim’, s limit and ideal limits, the ideal Cauchy sequences, and various specific spaces of triple sequences with respect to IFMS.

In many optimization problems, all decision-makers are not on the same level, but decision-makers may be placed in a hierarchical structure.‏ ‎Also, it is possible that the parameters of the problem are not stated crisp, but are presented in different types of fuzzy or interval. ‎In this study‎, ‎we considered ‎two‎ ‎‎‎state of the bilevel linear programming problems with ambiguity uncertainty.‎‏‎ In one of the problems, ‎all‎ the parameters were trapezoidal Intuitionistic fuzzy numbers, and in the other, ‎all‎ the parameters were triangular Intuitionistic fuzzy numbers. By using the proposed ranking method, we obtain the ‎‎‎bilevel linear programming problem corresponding to each state, which is solved by the usual methods.

The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Cesàro summability in an Intuitionistic fuzzy $n$-normed linear space (IFnNLS). We show that Cesàro summability method is regular in an IFnNLS, but  Cesàro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.

In this paper the solution of a second order linear differential equations with Intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.

The aim of this research paperto use the concept of Intimate mappings to demonstrate the existence and uniqueness of common fixed point theorems for self-mappings in Intuitionistic fuzzy metric space.