Sequences Of Fuzzy Numbers Research Articles

On the logarithmic summability method for sequences of fuzzy numbers

We define logarithmic summability method for sequences of fuzzy numbers and prove theorems dealing with the convergence behavior of logarithmic summable sequences of fuzzy numbers. The study also reveals slowly decreasing and Landau one-sided type Tauberian results analogous to those given by Moricz (Stud Math 219:109–121, 2013).

On Tauberian theorems for Cesàro summability of sequences of fuzzy numbers

In this paper we use the concept of the Cesaro convergence of a sequence of fuzzy numbers defined by Subrahmanyam [Cesaro summability of fuzzy real numbers, Anal, 7 (1999), 159–168] to prove some Tauberian theorems for sequences of fuzzy numbers and obtain fuzzy analogues of some classical Tauberian theorems for Cesaro summability of sequences of fuzzy numbers as a corollary.

I θ -statistical and p-Cesàro summability of sequences of fuzzy numbers

In this paper, following a very recent and new approach of [1, 2], the concept of lacunary strongly p-Cesàro summability of a sequence with order α of fuzzy number is introduced by using ideal. In addition to this concept, inclusion theorems are also presented. The study leaves some interesting ope n problems.

On the Borel summability method of sequences of fuzzy numbers

In the current paper, we define Borel summability of sequences of fuzzy numbers and investigate Tauberian conditions under which Borel summable sequences of fuzzy numbers are convergent. Also, we give analogous Tauberian results for Borel summability method of series of fuzzy numbers.

Generalized statistically convergent sequences of fuzzy numbers

The main object of this paper is to define certain new spaces of statistically convergent and strongly summable sequences of fuzzy numbers. We give necessary and sufficient conditions for a sequence of fuzzy numbers to be fuzzy λ- statistically pre-Cauchy and fuzzy λ-statistically convergent. We also establish some inclusion relations between the associated sets w F (M, p, λ) and S F (λ) supported by some numerical examples.

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

Some sets of $\chi^{2}-$ summable sequences of Fuzzy Numbers Defined By A Modulus

In this paper we introduce the $\chi^{2}$ fuzzy numbers defined by a modulus, study some of their properties and inclusion results.

On statistical summability (N¯,P) of sequences of fuzzy numbers

In this paper we introduce the concept of statistical summability (N?,p) of sequences of fuzzy numbers. We also present Tauberian conditions under which statistical convergence of a sequence of fuzzy numbers follows from its statistical summability (N?,p). Furthermore, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of statistical summability (N?,p).

On some difference sequence spaces of fuzzy numbers

In this paper, using the difference operator of order m and a lacunary sequence $$\theta = (k_{r})$$ź=(kr), we introduce and examine some classes of sequences of fuzzy numbers. Furthermore, we study some of their properties like completeness, solidity, symmetricity and convergence free. We also give some inclusion relations related to these classes.

Bounded variation of sequences of fuzzy numbers by using generalized weighted mean

A new class of bounded variation of sequences of fuzzy numbers by using generalized weighted mean is introduced. It is shown that this class forms a complete quasilinear metric space under some suitable metric. Further, various properties such as solidness, symmetric etc are investigated.

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.

Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function

The purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $Delta$ and give some inclusion relations.

Almost statistical convergence of order $$\beta $$ β of sequences of fuzzy numbers

In this article, we introduce the concepts of almost $$\lambda $$ź-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$źp-summability of order $$\beta $$β for sequences of fuzzy numbers. Also, we establish some relations between the almost $$\lambda $$ź-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$źp-summability of order $$\beta $$β and we define $$\hat{w}_{\lambda }^{\beta }\left( \mathcal {F},f,p\right) $$w^źβF,f,p, where $$f$$f is a modulus function and give some inclusion relations.

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

In this paper, a Tauberian theorem of slowly decreasing type is proved for the weighted mean method of summability of sequences of fuzzy numbers.

On $$\lambda $$ λ -statistical boundedness of order $$\beta $$ β of sequences of fuzzy numbers

On $$\lambda $$ λ -statistical boundedness of order $$\beta $$ β of sequences of fuzzy numbers

Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis

We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the(t1,t2)type fuzzy number. By defining the algebraic operations on the(t1,t2)type fuzzy numbers we can solve the equations in the formx+u(t1,t2)=v(t1,t2), whereu(t1,t2)andv(t1,t2)are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers[l∞(Ft)]B(r^,s^),[c(Ft)]B(r^,s^), and[c0(Ft)]B(r^,s^), consisting of all sequencesu∗=(u(t1,t2)k)such thatBr^,s^u∗is in the spacesl∞(Ft),c(Ft), andc0(Ft), have been constructed, respectively. Furthermore, some classes of matrix transformations from the spacecFtB(r^,s^)andμ(Ft)toμ(Ft)andcFtB(r^,s^)are characterized, respectively, whereμ(Ft)is any sequence space.

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

In this paper, a Tauberian theorem of slowly decreasing type is proved for the weighted mean method of summability of sequences of fuzzy numbers.

Almostλr-Statistical and Strongly Almostλr-Convergence of Orderβof Sequences of Fuzzy Numbers

The main purpose of this article is to introduce the concepts of almostλr-statistical convergence and strongly almostλr-convergence of orderβof sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almostλr-convergence and almostλr-statistical convergence of orderβof sequences of fuzzy numbers.

Some new sets of sequences of fuzzy numbers with respect to the partial metric.

In this paper, we essentially deal with Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh's extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the set of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine the relationships between these sets and their classical forms and give some properties including definitions, propositions, and various kinds of partial metric spaces of fuzzy level sets. Furthermore, we study some of their properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy level sets with respect to the partial metric based on a partial ordering.

Abel summability of sequences of fuzzy numbers

In the present study, we have introduced the concept of Abel summability for sequences and series of fuzzy numbers. Also, some tauberian results in classical analysis have been generalized to fuzzy analysis.