Intuitionistic Fuzzy Normed Spaces Research Articles

ROUGH IDEAL CONVERGENCE OF DOUBLE SEQUENCES IN INTUITIONISTIC FUZZY NORMED SPACES

The idea of rough statistical convergence for double sequences was studied by Ozcan and Or [34] in a intuitionistic fuzzy normed space. Recently the same has been generalized in the ideal context by Hossain and Banerjee [17] for sequences. Here in this paper we have discussed the idea of rough ideal convergence of double sequences in intuitionistic fuzzy normed spaces generalizing the idea of rough statistical convergence of double sequences. Also we have defined rough I2-cluster points for a double sequence and also investigated some of the basic properties associated with rough I2-limit set of a double sequence in a intuitionistic fuzzy normed space.

Rough Ideal Statistical Convergence via Generalized Difference Operators in Intuitionistic Fuzzy Normed Spaces

Rough Ideal Statistical Convergence via Generalized Difference Operators in Intuitionistic Fuzzy Normed Spaces

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

In this study, we define lacunary Δm-statistical convergence in the framework of intuitionistic fuzzy normed spaces (IFNS) for triple sequences. We prove several results for lacunary Δm-statistical convergence of triple sequence in IFNS. We further established lacunary Δm-statistical Cauchy sequences and provided the Cauchy convergence criterion for this novel idea of convergence.

Some Results on Nörlund ℐ2-Lacunary Statistical Convergent Sequences in Intuitionistic Fuzzy Normed Spaces

The intent of this paper is to investigate the intuitionistic Nörlund [Formula: see text]-lacunary statistically convergent sequence space. We present some intuitionistic fuzzy normed spaces (IFNS) in Nörlund convergent spaces. Moreover, we also put forward several topological and algebraic properties of these convergent sequence spaces.

Topological Properties of Jordan Intuitionistic Fuzzy Normed Spaces

AbstractThe article delves into the task of formulation of meticulous sequence spaces whose elements’ convergence is a generalized version of the Cauchy convergence in the setting of intuitionistic fuzzy norm. The task of attaining a finite limit is attained via an infinite matrix operator, namely, Jordan totient operator. We discuss some topological and algebraic properties and establish some inclusion relations between the spaces.

Some observations on Nörlund ℐ2-statistical convergence of double sequences in intuitionistic fuzzy normed spaces

The aim of this paper is to investigate the intuitionistic Nörlund [Formula: see text]-statistically convergent sequence space. We present some intuitionistic fuzzy normed spaces (IFNS) in Nörlund convergent spaces. Moreover, we also put forward several topological and algebraic properties of these convergent sequence spaces.

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.

A Study on Statistical Convergence of Triple Sequences in Intuitionistic Fuzzy Normed Space

A Study on Statistical Convergence of Triple Sequences in Intuitionistic Fuzzy Normed Space

Invariant convergent and invariant ideal convergent sequence in intuitionistic fuzzy normed space

The main purpose of this paper is to introduce invariant convergence in intuitionistic fuzzy normed space. Following which we present some characteristics of this notion with respect to intuitionistic fuzzy norm. We also define strongly invariant convergence, ideal invariant convergence and invariant ideal convergence in intuitionistic fuzzy normed space. After that, we establish the relationship between these notions with respect to intuitionistic fuzzy norm. Lastly, we define ideal invariant Cauchy and invariant ideal Cauchy criteria for sequences in intuitionistic fuzzy normed space and relate it to their convergence notion.

Tauberian theorems for weighted means of double sequences in intuitionistic fuzzy normed spaces

We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces(IFNS), and obtain necessary and sufficient Tauberian conditions under which convergence of double sequences in IFNS follows from their weighted mean summability. This study reveals also Tauberian results for some known summation methods in the special cases.

On (λ,μ,ζ)-Zweier ideal convergence in intuitionistic fuzzy normed spaces

In this paper, we introduce and study a new type of convergence which is namely (?,?,?)-Zweier convergence and (?,?,?)-Zweier ideal convergence of triple sequences x = (xijk) in intuitionistic fuzzy normed spaces (IFNS), where ?= (?n), ? = (?m) and ? = (? p) are three non-decreasing sequences of positive real numbers such that each tend to infinity. Besides, we define and study (?,?,?)-Zweier Cauchy and (?,?,?)- Zweier ideal Cauchy sequences on the said space and establish some relations among Them. problem.

On ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator

The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI (μ,ν)(T ) and 3SI0(μ,ν)(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.

ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.

Intuitionistic fuzzy stability results of additive functional equation by two different approaches

In this current work, we examine the Hyers-Ulam(H-U) stability results for a finite variable additive functional equation (Ref.[6]) in Intuitionistic Fuzzy Normed space(IFN-space) is discussed by means of direct and fixed point methods.

Tauberian theorems for statistical Cesàro and statistical logarithmic summability of sequences in intuitionistic fuzzy normed spaces

We define statistical Cesàro and statistical logarithmic summability methods of sequences in intuitionistic fuzzy normed spaces(IFNS) and give slowly oscillating type and Hardy type Tauberian conditions under which statistical Cesàro summability and statistical logarithmic summability imply convergence in IFNS. Besides, we obtain analogous results for the higher order summability methods as corollaries. Also, two theorems concerning the convergence of statistically convergent sequences in IFNS are proved in the paper.

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On Properties of Ideal Convergent Sequences in Jordan Intuitionistic Fuzzy Normed Spaces

On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces

We introduce logarithmic summability in intuitionistic fuzzy normed spaces($IFNS$) and give some Tauberian conditions for which logarithmic summability yields convergence in $IFNS$. Besides, we define the concept of slow oscillation with respect to logarithmic summability in $IFNS$, investigate its relation with the concept of q-boundedness and give Tauberian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between Ces\`{a}ro summability method and logarithmic summability method in $IFNS$ is also proved in the paper.

On some topological properties of intuitionistic $2$-fuzzy $n$-normed linear spaces

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.

On (λ,μ)- Zweier ideal convergence in intuitionistic fuzzy normed space

In this paper, we study and introduce a new type of convergence, namely (?,?)- Zweier convergence and (?,?)- Zweier ideal convergence of double sequences x = (xij) in intuitionistic fuzzy normed space (IFNS), where ? = (?n) and ?= (?m) are two non-decreasing sequences of positive real numbers such that each tending to infinity. Furthermore, we studied (?,?)- Zweier Cauchy and (?,?)- Zweier ideal Cauchy sequences on the said space and established a relation between them.

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c_{0}^{I}(hat{F}), c^{I}(hat{F}) and l_{infty }^{I}(hat{F}). In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (mu ,nu ). Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.