Difference Sequences Of Fuzzy Numbers Research Articles

On Deferred Statistical Convergence of Fuzzy Difference Sequence and Applications

In this paper, we introduce the idea of deferred statistical convergence using fractional difference operator of order [Formula: see text] for the sequence of fuzzy numbers. Also, we establish some relations between this idea and the strong deferred-summable fractional difference sequences of fuzzy numbers. As an application, we apply the idea of newly defined statistical convergence for proving fuzzy Korovkin-type approximation theorem.

Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1.

Lacunary sequences related to statistical convergence

In this manuscript, our concern is to introduce the new approach of studying the lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of fuzzy numbers. Some interesting and basic properties concerning them will be studied.

Applications of Tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers

Applications of Tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers

Fuzzy p-Absolutely Summable Difference Sequences

In this work, we introduce the notion of [Formula: see text]-absolutely summability of difference sequences of fuzzy numbers and then reduce the concept of [Formula: see text]-absolutely summable sequences of fuzzy numbers. We discuss the sets of such sequences of fuzzy numbers under different fuzzy metrics. We also establish the completeness under suitable metric. Examples along with suitable explanation are incorporated to make the theory of this paper interesting and useful. Finally, the concepts of fuzzy solidity and fuzzy symmetricity are defined and the classes for these two properties are examined as well.

Lacunary statistical convergence of order β in difference sequences of fuzzy numbers

In this paper, we define the spaces N β θ (p, F, � m ) ,S β (F, � m ) ,w β (F, � m ) for sequences of fuzzy numbers using generalized difference operatorm and a lacunary sequence θ and give some relations between them, where β ∈ (0, 1) and p> 0. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces S β θ (F, � m ) and w β (θ, f, F, � m ) according to modulus function f .

λ almost difference sequences of fuzzy numbers

In this study, we introduce several sets of sequences of fuzzy numbers using various sequencesrelations among these sets.and in the classand examine some inclusion

New type of generalized difference sequence of fuzyy numbers involving lacunary sequences

In this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers involving lacunary sequences. We give the relations between the lacunary strongly almost Cesaro type convergence and lacunary almost statistical convergence. Furthermore, we study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to these classes.

On Some New Generalized Difference Sequence Space of Fuzzy Numbers and Statistical Convergence

The main aim of the present paper is to introduce the concept of lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of Fuzzy numbers. We also investigate their some basic topological properties.

Statistical convergence of order β for generalized difference sequences of fuzzy numbers

In this study we introduce the concepts of Δm-statistical convergence of order β and strong $\Delta_{p}^{m}$-Cesaro summability of order β for sequences of fuzzy numbers by helping many examples. Also, we establish some properties which are valid for sequences of real numbers, but not for sequences of fuzzy numbers.

Lacunary difference ideal convergent sequence spaces of fuzzy numbers

In this article, using the Orlicz function M and the difference operator of order n ≥ 1, we introduce the spaces of lacunary ideal convergent difference sequences and lacunary strongly summable difference sequences of fuzzy numbers via fuzzy metric. We also established some relations related to these spaces. Further, we study some basic topological properties of these spaces.

On fuzzy real valued generalized difference I-convergent sequence spaces defined by Musielak-Orlicz function

In this article, using the Musielak-Orlicz function $\mathbf{M}$ and the difference operator, we introduce the spaces of I-convergent generalized difference sequences of fuzzy numbers. We prove the completeness of these spaces. Further, we investigate some inclusion relations related to these spaces.

Lacunary Statistical Limit and Cluster Points of Generalized Difference Sequences of Fuzzy Numbers

The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences are obtained.

On the class of λ-statistically convergent difference sequences of fuzzy numbers

In this study, we introduce the sets $$\left[ V,\lambda ,p\right] _{\Updelta }^{{\mathcal{F}}},\left[ C,1,p\right] _{\Updelta }^{{\mathcal{F}}}$$ and examine their relations with the classes of $$ S_{\lambda }\left( \Updelta ,{\mathcal{F}}\right)$$ and $$ S_{\mu }\left( \Updelta ,{\mathcal{F}}\right)$$ of sequences for the sequences $$\left( \lambda _{n}\right)$$ and $$\left( \mu _{n}\right) , 0<p<\infty $$ and difference sequences of fuzzy numbers.

COMPUTATION OF THE KÖTHE-TOEPLITZ DUAL OF SOME SETS OF SEQUENCES OF FUZZY NUMBERS

The main aim of the present paper is to compute the α–dual (or Köthe-Toeplitz dual) for some sets of sequences of fuzzy numbers defined using an Orlicz function. We also compute the α–dual of some sets of difference sequences of fuzzy numbers.

Some classes of difference sequences of fuzzy numbers defined by a sequence of Moduli

In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

On some sets of difference sequences of fuzzy numbers

In this paper we define the sequence space $${w}_{{\mathcal{F}}}\left(f,p,\Updelta\right)$$ which is called the space of strongly $$\Updelta p$$ -Cesaro summable sequences with modulus f. Furthermore the fuzzy Δ-statistically pre-Cauchy sequence is defined and the necessary and sufficient conditions are given for a sequence of fuzzy numbers to be fuzzy $$\Updelta$$ -statistically pre-Cauchy and to be fuzzy $$\Updelta$$ -statistically convergent. Also some relations between $$w_{{\mathcal{F}}}(f,p,\Updelta)$$ and $${S}_{{\mathcal{F}}}(\Updelta)$$ are given.

On Lacunary Almost Statistical Convergence of Generalized Difference Sequences of Fuzzy Numbers

The purpose of this paper is to introduce the concepts of lacunary almost statistical convergence and strongly almost convergence of generalized difference sequences of fuzzy numbers. We obtain some results related to these concepts. It is also shown that lacunary almost △(superscript m)θ- statistical convergence and strongly almost △(superscript m)θ- convergence are equivalent for △(superscript m)- bounded sequences of fuzzy numbers.

Generalized difference sequences of fuzzy numbers

The idea of difference sequences of real (or complex) numbers was generalized by Et and Çolak [Et M, Çolak R. On some generalized difference sequence spaces. Soochow J Math 1995; 21(4): 377–86; Çolak R, Et M. On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math J 1997; 26(3): 483–92]. In this paper, using the difference operator Δ m and an Orlicz function, we introduce and examine some sequence spaces of fuzzy numbers. We study some of their properties like completeness, solidity, symmetricity, etc. We also give some relations related to these spaces.

Lacunary Statistical and Lacunary Strongly Convergence of Generalized Difference Sequences of Fuzzy Numbers

The purpose of this paper is to introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences of fuzzy numbers. We give some relations related to these concepts. We show that lacunary Δ m -statistical convergence and lacunary strongly Δ ( p ) m -convergence are equivalent for Δ m -bounded sequences of fuzzy numbers. We also introduce the concept of lacunary Δ m -statistically Cauchy sequence and show that it is equivalent to the lacunary Δ m -statistical convergence.