scholarly journals On the Cesàro convergence of sequences of fuzzy numbers

2012 ◽  
Vol 25 (4) ◽  
pp. 676-681 ◽  
Author(s):  
Özer Talo ◽  
Celal Çakan
Keyword(s):  
Fuzzy Numbers ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Cesaro Convergence

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.

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.

scholarly journals Rough statistical convergence of sequences of fuzzy numbers

Mathematica ◽  
2019 ◽  
Vol 61 (84) (1) ◽  
pp. 33-39
Author(s):  
Shyamal Debnath ◽  
◽  
Debjani Rakshit ◽  
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

scholarly journals On the Slowly Decreasing Sequences of Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Özer Talo ◽  
Feyzi Başar
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Tauberian Condition ◽  
Sequences Of Fuzzy Numbers ◽  
Slowly Decreasing Sequences ◽  
Cesaro Convergence

We introduce the slowly decreasing condition for sequences of fuzzy numbers. We prove that this is a Tauberian condition for the statistical convergence and the Cesáro convergence of a sequence of fuzzy numbers.

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