Intuitionistic Fuzzy Averaging Research Articles

Intuitionistic Type-2 Fuzzy Normed Linear Space and Some of Its Basic Properties

Intuitionistic Type-2 Fuzzy Normed Linear Space and Some of Its Basic Properties

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.

Fibonacci Lacunary Ideal Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces

The purpose of this article is to research the concept of Fibonacci lacunary ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces (IFNS). Additionally, a new concept, called Fibonacci lacunary convergence, is examined. Also, Fibonacci lacunary I₂-limit points and Fibonacci lacunary I₂-cluster points for double sequences in IFNS have been defined and the significant results have been given. Additionally, Fibonacci lacunary Cauchy and Fibonacci lacunary I₂-Cauchy double sequences are worked.

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.

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.

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.

A new intuitionistic fuzzy definiteness norm

In the present paper we introduce a new intuitionistic fuzzy norm over intuitionistic fuzzy pairs and study some of its properties.

Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.

New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature.

Generalized weighted statistical convergence in intuitionistic fuzzy normed linear spaces

In this paper, we introduce a new statistical convergence type, named weighted λ-statistical convergence to generalize the concept of weighted statistical convergence with respect to the intuitionistic fuzzy norm (µ, υ). Moreover, we establish its relation to weighted statistical convergence and a new summability method, named as Nλ, p -summability with respect to the intuitionistic fuzzy norm (µ, υ).

A Clustering Algorithm Based on Intuitionistic Fuzzy Relations for Tree Structure Evaluation

Intuitionistic fuzzy relations are used to construct hierarchical structures for the evaluation of vague complicated humanistic systems. A novel algorithm to develop partition trees at different levels according to different intuitionistic fuzzy triangular norm composition is presented. Examples are given to demonstrate the usefulness of the proposed algorithm.

On Generalized Double Statistical Convergence of Order α in Intuitionistic Fuzzy Normed Spaces

Our goal in this work is to introduce the notion V , λ ( I ) 2 -summability and ideal λ-double statistical convergence of order α with respect to the intuitionistic fuzzy norm μ , v . We also make some observations about these spaces and prove some inclusion relations.

Aggregating evaluation using dynamic weighted intuitionistic fuzzy approach for concept sequencing in an e-learning system

Adaptation of learning concepts in an e-learning system for individuals depends on his ability to learn. Learners are perplexed in hyperspace when learning concepts are displayed in an unstructured form. To provide an effective learning path, sequencing of learning concepts and contents should be according to learner's orientation and individualised access support. Therefore to reduce disorientation, each learner should get path based on his level of knowledge acquisition and learning style. However, most of the e-learning systems determine the learner's knowledge through expert weight given to a learning concept whereas in this work weights of learning concepts are determined during learners' assessment itself. For this, we applied intuitionistic fuzzy theory approach and proposed a dynamic weighted concept intuitionistic fuzzy averaging (DWCIFA) operator to personalise the sequencing of learning concepts based on assessment results. We tested the algorithm on synthetic data set, created using quasi random generator function in Python. The results prove that it improves navigation, and also helps student to achieve deep knowledge in the domain.

Generalized Statistical Convergence in Intuitionistic Fuzzy 2− Normed Space

In this paper, we shall introduce the new notion namely, I -λ statistical convergence by using ideal with respect to the intuitionistic fuzzy norm (μ, v)2. We also study the relation between I -λ statistical convergence and I -statistical convergence. subjclass(2000) 40A05; 40B50; 46A19; 46A45.

Lacunary Statistical Convergence of Multiple Sequences in Intuitionistic Fuzzy Normed Spaces

In this paper we introduce the notion ideal statistical convergence and ideal lacunary statistical convergence of multiple sequences with respect to the intuitionistic fuzzy norm (μ, v), investigate their relationships, and make some observations about these classes.

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces