Convergent Sequences Of Fuzzy Numbers Research Articles

Logarithmic means of sequences of fuzzy numbers and a Tauberian theorem

A sequence $$(x_n)$$ of fuzzy numbers is said to be summable to a fuzzy number L by the logarithmic mean method $$(\ell ,2)$$ if $$\begin{aligned} \lim _{n\rightarrow \infty }\frac{1}{\ell _n^{(2)}}\sum _{k=1}^{n}\frac{x_k}{k\ell _k}=L \end{aligned}$$where $$\begin{aligned} \ell _n^{(2)}=\sum _{k=1}^{n}\frac{1}{k\ell _k}\sim \log (\log n). \end{aligned}$$We prove that the ordinary convergence of $$(x_n)$$ implies its $$(\ell ,2)$$ summability. The converse implication is not necessarily true. Namely, the $$(\ell ,2)$$ summability of $$(x_n)$$ may not imply the convergence of $$(x_n)$$. However, under certain additional conditions the converse may hold. Such conditions are called Tauberian conditions, and the resulting theorem is said to be a Tauberian theorem. In this paper, we provide necessary and sufficient Tauberian conditions to transform $$(\ell ,2)$$ summable sequences of fuzzy numbers into convergent sequences of fuzzy numbers with preserving the limit.

Tauberian theorems for statistical summability methods of sequences of fuzzy numbers

We give Tauberian conditions of slow decrease type under which statistical Cesaro summability and statistical logarithmic summability of sequences of fuzzy numbers imply convergence in fuzzy number space. Besides, we obtain a sufficient condition for statistically convergent sequences of fuzzy numbers to converge in the ordinary sense.

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.

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.

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.

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.

On λ− summable entire sequences of fuzzy numbers

In this paper the concept of strongly ( λ )_ p − Cesa ro summability of a sequence of fuzzy numbers and strongly λ − statistically convergent sequences of fuzzy numbers are introduced.

Nörlund and Riesz mean of sequences of fuzzy real numbers

In this article we study some properties of the Nörlund and Riesz mean of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for the Nörlund and Riesz means to transform convergent sequences of fuzzy numbers into convergent sequences of fuzzy numbers with limit preserving.

ON ALMOST CONVERGENT SEQUENCES OF FUZZY NUMBERS

In this paper, we study the space of almost convergent sequences of fuzzy numbers and show that it is complete metric space. We also introduce and discuss the concept of almost statistical convergence of fuzzy numbers.

On λ-statistical convergence of difference sequences of fuzzy numbers

In this paper the concept of strongly Δ λ p 2 -Cesàro summability of a sequence of fuzzy numbers is introduced. Also some inclusion relations between the set of strongly Δ λ p 2 -Cesàro convergent and Δ λ 2 -statistically convergent sequences of fuzzy numbers are given.

Remark on lacunary statistical convergence of fuzzy numbers

Fatih Nuray [Fuzzy Sets and Systems 99(3) (1998) 269] proved the inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. In this paper we show that Nuray's condition is sufficient as well as necessary.

On statistically convergent sequences of fuzzy numbers

In this paper we study some equivalent alternative conditions for a sequence of fuzzy numbers to be statistically Cauchy.

On Statistically Convergent Sequences of Fuzzy Numbers

In this paper, some equivalent alternative conditions are obtained for a sequence of fuzzy numbers to be statistically Cauchy.

Lacunary statistical convergence of sequences of fuzzy numbers

The sequence X = { X k } of fuzzy numbers is statistically convergent to the fuzzy number X 0 provided that for each ϵ ≺ 0 lim l n { the number ofk⩽n:d(X k,X 0)⩾ϵ}=0 . In this paper we study a related concept of convergence in which the set { k: k⩽ n} is replaced by { k: k r−1 ≺ k ⩽ k r } for some lacunary sequence { k r }. Also we introduce the concept of lacunary statistically Cauchy sequence and show that it is equivalent to the lacunary statistical convergence. In addition, the inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers are given.