Lacunary statistical convergence of sequences of fuzzy numbers

1998 ◽  
Vol 99 (3) ◽  
pp. 353-355 ◽  
Author(s):  
Fatih Nuray
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

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.

ON ASYMPTOTICALLY LACUNARY σ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

2009 ◽  
Vol 05 (03) ◽  
pp. 589-598 ◽  
Author(s):  
EKREM SAVAŞ
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Invariant Mean ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

This paper presents the asymptotically lacunary σ-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary σ-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.

scholarly journals Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers - doi: 10.5269/bspm.v30i2.14007

2011 ◽  
Vol 30 (2) ◽  
pp. 57-62
Author(s):  
Ayhan Esi ◽  
Necdet Çatalbas
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Lacunary Sequence ◽  
Lacunary Statistical Convergence ◽  
Sequences Of Fuzzy Numbers ◽  
Natural Combination

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let =(k_{r}) be a lacunary sequence. The two sequnces X  = (X_{k}) and Y=(Y_{k}) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every >0lim_{r}(1/(h_{r}))|{k∈I_{r}:d(((X_{k})/(Y_{k})),L)≥}|=0. 

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
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