On the ideal convergence of sequences of fuzzy numbers

2008 ◽  
Vol 178 (24) ◽  
pp. 4670-4678 ◽  
Author(s):  
Vijay Kumar ◽  
Kuldeep Kumar
Keyword(s):  
Fuzzy Numbers ◽  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
The Ideal

scholarly journals On the almost everywhere statistical convergence of sequences of fuzzy numbers

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2683-2693 ◽  
Author(s):  
Özer Talo
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Almost Everywhere ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

In this paper, we define the concept of almost everywhere statistical convergence of a sequence of fuzzy numbers and prove that a sequence of fuzzy numbers is almost everywhere statistically convergent if and only if its statistical limit inferior and limit superior are equal. To achieve this result, new representations for statistical limit inferior and limit superior of a sequence of fuzzy numbers are obtained and we show that some properties of statistical limit inferior and limit superior can be easily derived from these representations.

I-CONVERGENCE OF SEQUENCES OF FUZZY NUMBERS

2008 ◽  
Vol 04 (02) ◽  
pp. 231-236 ◽  
Author(s):  
FATIH NURAY
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Number Sequences ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
Cluster Points

In this study, the concepts of I-convergent, I-Cauchy, I-bounded, I-limit points and I-cluster points for fuzzy number sequences have been introduced and discussed.

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

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 849-858 ◽  
Author(s):  
Özer Talo ◽  
Celal Çakan
Keyword(s):  
Fuzzy Numbers ◽  
Bounded Sequence ◽  
Tauberian Theorems ◽  
Tauberian Conditions ◽  
Statistical Limit ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient ◽  
Convergent Sequences

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.

Weighted uniform density ideals

2018 ◽  
Vol 68 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Jacek Tryba
Keyword(s):  
Uniform Density ◽  
Topological Complexity ◽  
Ideal Convergence ◽  
Darboux Property ◽  
Analytical Properties ◽  
Banach Density ◽  
Convergence Of Sequences ◽  
The Ideal

Abstract Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of weighted uniform density ideals and consider the topological complexity of these ideals as well as when they have certain analytical properties related to the ideal convergence of sequences and series. Furthermore, we prove some inequalities between different upper and lower weighted uniform densities and give the answer to the problem concerning the Darboux property of these densities.

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

2021 ◽  
pp. 1-10
Author(s):  
Sonali Sharma ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Matlab Software ◽  
Difference Sequences ◽  
Cesaro Summability ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Theoretical Results

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.

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