Sequences Of Fuzzy Numbers Research Articles

The dynamics and behavior of logarithmic type fuzzy difference equation of order two.

Fuzzy difference equations are becoming increasingly popular in fields like engineering, ecology, and social science. Difference equations find numerous applications in real-life problems. Our study demonstrates that the logarithmic-type fuzzy difference equation of order two possesses a nonnegative solution, and an equilibrium point, and exhibits asymptotic behavior. [Formula: see text] Where, xi represents the sequence of fuzzy numbers, and the parameters α, β, A, along with the initial conditions x-1 and x0, are positive fuzzy numbers. The characterization theorem is employed to convert each single logarithmic fuzzy difference equation into a set of two crisp logarithmic difference equations within a fuzzy environment. We evaluated the stability of the equilibrium point of the fuzzy system. Utilizing variational iteration techniques, the method of g-division, inequality skills, and a theory of comparison for logarithmic fuzzy difference equations, we investigated the governing equation dynamics, including its boundedness, existence, and both local and global stability analysis. Additionally, we provided some numerical solutions for the equation describing the system to verify our results.

Retraction Note: Statistical harmonic summability of sequences of fuzzy numbers

Retraction Note: Statistical harmonic summability of sequences of fuzzy numbers

A Framework for I*-Statistical Convergence of Fuzzy Numbers

In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*−liminf.

Almost lacunary statistical and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers

The main purpose of this article is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost lacunary convergence and almost lacunary statistical convergence of order (β,γ) of sequences of fuzzy numbers, where β and γ are two fixed real numbers such that 0 β≤γ≤1.

ON ρ-STATISTICAL CONVERGENCE OF SEQUENCES OF FUZZY NUMBERS

In this study, we present the concepts of ρ-statistically convergence for sequences of fuzzy numbers as well as strong (w_ρ (F)) summability and ρ-Cauchy statistically convergence for sequences of fuzzy numbers. We also provide several results concerning these concepts.

On ρ-Statistically Convergence Defined by a Modulus Function in Fuzzy Difference Sequences

In this study, we first introduced the definition ∆_ρ^m-statistical convergence for sequences of fuzzy numbers using the generalized difference operator ∆^m. Furthermore, we defined the strong N_F^ρ (∆^m,q)-summable sequence set and the strong N_F^ρ (∆^m,f,q)-summable sequence set for fuzzy difference sequences aided by a modulus function f. Subsequently, we provided certain inclusion theorems between these sets and the S_F^ρ (∆^m ) set.

New Tauberian Theorems for Cesáro Summable Triple Sequences of Fuzzy Numbers

The purpose of this paper is to establish new results on Tauberian theorem for Cesàro summability of triple sequences of fuzzy numbers. Besides, we extend and unify several results in the available literature. Furthermore, a huge number of special cases, theorems and their implications are proved. We show some illustrative examples in support of the results obtained in this paper.

Statistical Riesz and Nörlund convergence for sequences of fuzzy numbers

Nuray and Savaş proposed statistical convergence of fuzzy number sequences. Afterward, Tripathy and Baruah presented Riesz and Nörlund convergence for sequences of fuzzy numbers. This paper defines statistical Riesz and Nörlund convergence of fuzzy number sequences. It then shows that if a sequence of fuzzy numbers is convergent, then it is statistical Riesz/Nörlund convergent, but the converse is not always true. Finally, this paper discusses the need for further research.

ON ρ-STATISTICAL CONVERGENCE OF ORDER (α,β) FOR SEQUENCES OF FUZZY NUMBERS

In this study, we first give the definition of ρ-statistical convergence of order (α,β) for sequences of fuzzy numbers. We also define the strongly w(ρ,F,q)-summable of order (α,β) and the strongly w(ρ,F,q,f)-summable of order (α,β), defined by a modulus function f for sequences of fuzzy numbers. Later we give some coverage theorems between these sets and the set S_α^β (ρ,F).

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

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

$\Delta^{f}-$lacunary statistical boundedness of order $\beta$ for sequences of fuzzy numbers

In the present paper, we introduce the concept of $\Delta^{f}-$lacunary statistical boundedness of order $\beta$\ with respect to a modulus function $f$ for sequences of fuzzy numbers and give some relations between $\Delta^{f}-$lacunary statistical boundedness of order $\beta$\ and $\Delta^{f}-$statistical boundedness with respect to a modulus function $f$ with the help of many examples and figures. Furthermore, we study some properties like solidity, symmetricity, etc.

On regular variations of fuzzy sequences via deferred statistical convergence

This paper introduces the idea of deferred statistical convergence of order ? via the concept of regular variations of sequences of fuzzy numbers. The convergence of sequences of fuzzy numbers using ideas of variations such as regular, O?regular, translational regular and rapid, etc, are discussed in the context of deferred statistical convergence of order ?. Results on generating relations among these different fuzzy deferred statistical variations are established.

Generalized 𝝀 −Statistical Boundedness of Order 𝜷 in Sequences of Fuzzy Numbers

In this article, we investigate the idea of Δ_λ^m-statistical boundedness of order β for sequences of fuzzy numbers. Additionally, we provide different inclusion relations between Δ_λ^m-statistical boundedness of order β and Δ_λ^m-statistical convergence of order β.

On Statistical Convergence of Uncertain Sequence of Fuzzy Numbers

In this paper, we extend the various ideas of convergence such as convergence in distribution, in mean, and in measure along with the convergence uniformly almost surely of the uncertain fuzzy sequence of real numbers in statistical context. We also establish some interesting results among these convergence.

Kannan Nonexpansive Operators on Variable Exponent Cesàro Sequence Space of Fuzzy Functions

In general, we have constructed the operator ideal generated by extended s -fuzzy numbers and a certain space of sequences of fuzzy numbers. An investigation into the conditions sufficient for variable exponent Cesàro sequence space of fuzzy functions furnished with the definite function to create pre-quasi-Banach and closed is carried out. The R and the normal structural properties of this space are shown. Fixed points for Kannan contraction and nonexpansive mapping have been introduced. Lastly, we explore whether the Kannan contraction mapping has a fixed point in its associated pre-quasioperator ideal. The existence of solutions to nonlinear difference equations is illustrated with a few real-world examples and applications.

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.

Multidimensional Asymptotically Lacunary Statistical Equivalent of Order α for Sequences of Fuzzy Numbers

The main goal of this article is to present the notion of double asymptotically lacunary statistical equivalent of order α for sequences of fuzzy numbers by considering fuzzy numbers and Pringsheim limit. To accomplish this goal, we mainly investigate some fundamental properties of the newly introduced notion. Additionally, it should be note that some interesting inclusion theorems are examined and also new variations are presented.

On deferred-statistical convergence of uncertain fuzzy sequences

Uncertain theory which was initially introduced by Liu [2016. Unceratinty Theory. 5th ed. Berlin: Springer-Verlag] is significantly speared in various fields of engineering and scientific computing such as probability theory, statistics, fuzzy set theory, measure theory, summability theories, etc. As a part of this theory, the problems of convergence with different perspectives such as the idea of convergence in distribution, in mean and in measure along with the convergence uniformly almost surely of the sequence of complex numbers have been studied using uncertain variables. Later on, the results analogue to statistical convergence have been generalized and studied by Tripathy and Nath [2017. “Statistical Convergence of Complex Uncertain Sequences.” New Mathematics and Natural Computation 13 (3): 359–374.]. In this paper, we indent to extend the investigation for the sequences of fuzzy numbers and study the uncertainty of the above ideas of convergence via deferred Cesàro mean. Certain results on deferred-statistical convergence of order for real uncertain sequences are established.

On Statistical Limit Points in a Fuzzy Valued Metric Space

We introduce the concepts statistical cluster and statistical limit points of a sequence of fuzzy numbers in a fuzzy valued metric space. Then we obtain some inclusion relations between the sets of limit points, statistical limit points and statistical cluster points for a sequence of fuzzy numbers.

Ideal statistically limit points and ideal statistically cluster points of triple sequences of fuzzy numbers

Ideal statistically limit points and ideal statistically cluster points of triple sequences of fuzzy numbers