Sequences Of Fuzzy Numbers Research Articles

Random metric space of fuzzy numbers

In this paper, we introduce the concept of a random metric (RM) space of fuzzy numbers and establish some of its basic properties. In this approach, the distance between two fuzzy numbers is considered as a certain measurable function. Using this concept, we also obtain some convergence relations for a sequence of fuzzy numbers. Finally, we investigate a boundedness property for a subset of such an RM space.

The statistical convergence for sequences of fuzzy-number-valued functions

Based on the concept of statistical convergence of sequences of fuzzy numbers, the statistical convergence, uniformly statistical convergence and equi-statistical convergence of sequences of fuzzy-number-valued functions are defined and investigated in this paper. The relationship among statistical convergence, uniformly statistical convergence, equi-statistical convergence of sequences of fuzzy-number-valued functions and their representations of sequences of α-level cuts are discussed. In addition, the Egorov and Lebesgue theorems for the statistical convergence of sequences of fuzzy-number-valued functions are obtained in a finite measure set. Finally, the statistical convergence in measure for sequences of fuzzy-number-valued functions is investigated, and it is proved that the outer and inner statistical convergence in measure are equivalent in a finite measure set for a sequence of fuzzy-number-valued functions.

Some conditions under which slow oscillation of a sequence of fuzzy numbers follows from Ces`{a}ro summability of its generator sequence

Let $(u_n)$ be a sequence of fuzzy numbers. We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

Relations between Lambda-Statistical Limit İnferior and Limit Superior for Sequences of Fuzzy Numbers

Relations between Lambda-Statistical Limit İnferior and Limit Superior for Sequences of Fuzzy Numbers

$$\lambda $$ λ -Statistical limit points of order $$\beta $$ β of sequences of fuzzy numbers

In this article, we introduce \(\lambda \)-statistical limit and cluster points of order \(\beta \) for sequences of fuzzy numbers. Also, we give some relations between them.

$\mathcal{I}$ and $\mathcal{I}^{\ast}$ convergence of multiple sequences of fuzzy numbers

Recently, the concept of statistical convergence for multiple sequences of fuzzy numbers has been studied by Kumar et al. This motivate us to extend the idea of $\mathcal{I}$-convergence to sequences of fuzzy numbers of multiplicity greater than two.

The extension of the Knopp core theorem to the sequences of fuzzy numbers

The concept of the core of a sequence of fuzzy numbers has been introduced by Aytar et al. in [The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159(24) (2008) 3369–3379]. Quite recently, some matrix transformations on the classical sets of sequences of fuzzy numbers have been characterized by Talo and Başar in [Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717–733]. In this paper, we have proved a core theorem for sequences of fuzzy numbers which is analogous to the famous Knoop Core Theorem for real sequences. To achieve this goal, we have studied some properties of the lim sup and lim inf of sequences of fuzzy numbers. Also, we have characterized a class of positive regular matrices of fuzzy numbers such that these matrices leave the core of any bounded sequence of fuzzy numbers invariant.

Tauberian theorems for statistically (C,1)-convergent sequences of fuzzy numbers

In this paper, we have determined necessary and sufficient Tauberian conditions under which statistically convergence follows from statistically (C,1)-convergence of sequences of fuzzy numbers. Our conditions are satisfied if a sequence of fuzzy numbers is statistically slowly oscillating. Also, under additional conditions it is proved that a bounded sequence of fuzzy numbers which is (C,1)-level-convergent to its statistical limit superior is statistically convergent.

On generalized statistical convergence of order β of sequences of fuzzy numbers

In this article we introduce the concepts of $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β for sequences of fuzzy numbers. Also, we establish some relations between the $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β and we define $w_{\lambda}^{\beta}\left\Delta^{m},\mathcal{F},f,p\right$, where $f$ is a modulus function and give some inclusion relations.

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.

Some I-convergent multiplier double classes of sequences of fuzzy numbers defined by Orlicz functions

In this paper using ideal I and Orlicz function M together with a general multiplier double sequence Λ = λnk, n, k ∈ N of non-zero real numbers, we introduce some new type of I-convergent fuzzy rea...

A new approach for the sequence spaces of fuzzy level sets with the partial metric

In this paper, we investigate the classical sets of sequences of fuzzy numbers by using partial metric which is based on a partial ordering. Some elementary notions and concepts for partial metric and fuzzy level sets are given. In addition, several necessary and sufficient conditions for partial completeness are established by means of fuzzy level sets. Finally, we give some illustrative examples and present some results between fuzzy and partial metric spaces.

On Casaro Sequence Space of Fuzzy Numbers Defined by a Modulus Function

The main purpose of this paper is to introduce the sequence space cesF(f, p) of sequence of fuzzy numbers defined by a modulus function. Furthermore, some inclusion theorems have been discussed.

Periodicity of the Positive Solutions of a Fuzzy Max-Difference Equation

We investigate the periodic nature of the positive solutions of the fuzzy max-difference equationxn+1=maxAn/xn-m,xn-k,n=0,1,…, wherek,m∈{1,2,…},Anis a periodic sequence of fuzzy numbers, andx-d,x-d+1,…,x0are positive fuzzy numbers withd=m,k. We show that every positive solution of this equation is eventually periodic with periodk+1.

Some I-convergent multiplier double classes of sequences of fuzzy numbers defined by Orlicz functions

In this paper using ideal I and Orlicz function M together with a general multiplier double sequence Λ = λnk, n, k ∈ N of non-zero real numbers, we introduce some new type of I-convergent fuzzy real-valued double sequence spaces. We have studied different topological properties of these sequence spaces. Also we have characterized the multiplier problem and some inclusion relations involving these classes of sequences are obtained. Further some equivalent statements involving these classes of sequences are established.

Tauberian theorems for Cesàro summability of sequences of fuzzy numbers

Tauberian theorems for Cesàro summability of sequences of fuzzy numbers

ON LACUNARY STATISTICAL LIMIT AND CLUSTER POINTS OF SEQUENCES OF FUZZY NUMBERS

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [S. Aytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci. 165 (2004) 129-138]. Later, we find restriction on the lacunary sequence $theta = (k_{r})$ for which the sets $Lambda^{F}_{S_{theta}}(X)$ and $Gamma^{F}_{S_{theta}}(X)$ respectively coincides with the sets $Lambda^{F}_{S}(X)$ and $Gamma^{F}_{S}(X)$.

<b>On almost λ- statistical convergence of fuzzy numbers</b> - doi: 10.4025/actascitechnol.v36i1.16218

The purpose of this paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ- convergence of fuzzy numbers. We obtain some results related to these concepts. It is also shown that almost λ- statistical convergence and strongly almost λ-convergence are equivalent for almost bounded sequences of fuzzy numbers.

Generalized lacunary Δ m -statistically convergent sequences of fuzzy numbers using a modulus function

In this paper, we introduce the space of lacunary strongly Δ ( p ) m -summable sequences of fuzzy numbers and discuss relations between Δ m -statistically convergent sequences and lacunary Δ m -statistically convergent sequences of fuzzy numbers. We also study inclusion relations using different arbitrary lacunary sequences.MSC:40A05, 40C05, 46A45.

Some Orlicz extended ℐ-convergent A-summable classes of sequences of fuzzy numbers

Abstract The article introduces some classes of sequences of fuzzy numbers extended by Orlicz functions by using the notions of ℐ-convergence and matrix transformation and investigates the classes for relationship between them as well as establishes some relevant properties. Further, the Hukuhara difference property is employed to derive a new kind of spaces and prove that such spaces can be equipped with a linear topological structure. MSC:40A05, 40D25, 40C05, 46A45.