Double Sequences Of Fuzzy Numbers Research Articles

Some observations on statistical convergence of uncertain double sequences of fuzzy numbers

Some observations on statistical convergence of uncertain double sequences of fuzzy numbers

Weighted (<i>λ</i>, <i>μ</i>)-Ideal Statistical Convergence and Strongly Weighted (<i>λ</i>, <i>μ</i>)-Ideal Convergence of Double Sequences of Fuzzy Numbers

The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ, μ)-ideal statistical convergence and strongly weighted (λ, μ)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.

Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.

New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

Fractional difference double sequences of fuzzy numbers

Fractional difference double sequences of fuzzy numbers

Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem

The paper aims to investigate different types of weighted statistical convergence and weighted statistical summability of double sequences of fuzzy numbers. Relations connecting statistical convergence and statistical summability have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. Relevant inclusion relations and related results concerning the new fuzzy summability methods have also been examined in detail. Finally, a Korovkin-type approximation theorem for double sequences of fuzzy positive linear operators has been established using the most generalized version of the summability method and showed its efficiency by means of a concrete example.

The core of a double sequence of fuzzy numbers

We present the concepts of the limit superior and the limit inferior of a double sequence of fuzzy numbers and obtain several properties of these concepts. By using these concepts we also characterize the core of a double sequence of fuzzy numbers as a closed interval. Furthermore, we define Γ-convergence and the endograph metric convergence for a double sequence of fuzzy numbers, which are new types of convergence and investigate the relations between these types of convergence and the core of the sequence.

Statistical weighted mean summability of double sequences of fuzzy numbers

In this paper, we present statistical weighted mean ( briefly, (N?,p,q,1,1)) summability method for double sequences of fuzzy numbers and give necessary and sufficient Tauberian conditions under which statistical convergence of a double sequence of fuzzy numbers follows from its statistical (N?,p,q,1,1) summability. Furthermore, we apply our new method of summability to prove a fuzzy Korovkin type approximation theorem for a double sequence of fuzzy positive linear operators.

Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vallée Poussin mean

Tauberian theorem serves the purpose to recuperate Pringsheim’s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vallée Poussin mean and double difference operator of order r . We prove that a bounded double sequence of fuzzy number which is Δ u r - convergent is ( C , 1 , 1 ) Δ u r - summable to the same fuzzy number L . We make an effort to develop some new slowly oscillating and Hardy-type Tauberian conditions in certain senses employing de la Vallée Poussin mean. We establish a connection between the Δ u r - Hardy type and Δ u r - slowly oscillating Tauberian condition. Finally by using these new slowly oscillating and Hardy-type Tauberian conditions, we explore some relations between ( C , 1 , 1 ) Δ u r - summable and Δ u r - convergent double fuzzy number sequences.

Results on Tauberian Theorem for Cesàro Summable Double Sequences of Fuzzy Numbers

The paper aims to establish new results on Tauberian theorem for Cesàro summability of double sequences of fuzzy numbers, and thus to extend and unify several results in the available literature. Further, a number of special cases, corollaries and illustrative example in support of the investigation of this paper are also presented.

Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

We define the notions of weighted λ,μ-statistical convergence of order γ1,γ2 and strongly weighted λ,μ-summability of γ1,γ2 for fuzzy double sequences, where 0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted λ,μ-statistical convergence of order γ1,γ2 to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

New Type Of Double Sequence of Fuzzy Numbers Defined on Double Orlicz Function

New Type Of Double Sequence of Fuzzy Numbers Defined on Double Orlicz Function

New type of Double Sequence of Fuzzy Numbers Defined on Double Orlicz Function

In this paper we insert the notion of -statistically,pre-Cauchy double sequence of fuzzy numbers also, we establish a criterion for arbitrary double sequence of fuzzy numbers to becomes -statistically,pre-Cauchy.

Statistical Convergence of order β for (λ, μ) double sequences of fuzzy numbers

In this study, we introduce the concepts of φλ,μ-double statistically convergence of order β in fuzzy sequences and strongly λ- double Cesaro summable of order β for sequences of fuzzy numbers. Also we give some inclusion theorems.

ROUGH CONVERGENCE OF DOUBLE SEQUENCES OF FUZZY NUMBERS

In this paper, we define the concepts of rough convergence and rough Cauchy sequence of double sequences of fuzzy numbers. Then, we investigate some relations between rough limit set and extreme limit points of such sequences.

Tauberian theorems for $$(\overline{N},p,q)$$ summable double sequences of fuzzy numbers

In this paper, we define the weighted mean method $$(\overline{N},p,q)$$ of double sequences of fuzzy numbers and give necessary and sufficient Tauberian conditions under which convergence in Pringsheim’s sense of a double sequence of fuzzy numbers follows from its $$(\overline{N},p,q)$$ summability. These conditions are weaker than the weighted analogues of Landau’s conditions and Schmidt’s slow oscillation condition in some senses for two-dimensional case.

Characterization of matrix classes involving some sets of summable double sequences of fuzzy numbers

Characterization of matrix classes involving some sets of summable double sequences of fuzzy numbers

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

Abstract In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively.

A Tauberian theorem for $(C,1,1)$ summable double sequences of fuzzy numbers

In this paper, we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.

Tauberian theorems for statistically convergent double sequences of fuzzy numbers

In this paper, we introduce slow oscillation and Hardy’s two-sided Tauberian conditions for double sequences in n-dimensional fuzzy number space En. Besides, slow decrease and Landau’s one-sided Tauberian conditions for double sequences in E1 are presented. Under these conditions we also prove Taub erian theorems for statistically convergent double sequences of fuzzy numbers.