The statistical convergence for sequences of fuzzy-number-valued functions

Gong, Zengtai; Zhang, Lu; Zhu, Xinyun

doi:10.1016/j.ins.2014.10.025

Cited by 14 publications

(8 citation statements)

References 15 publications

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“…This has been extended in case of fuzzy by several authors such as Nuray [10], Savas [11], Ojha and Srivastava [13] etc from several aspects. Recently, Gong et al [14] defined statistical convergence in measure for sequences of fuzzy functions and established Egorov and Lebesgue theorems in statistical sense.…”

Section: Preliminariesmentioning

confidence: 99%

Some characterizations on weighted $$\beta \gamma $$ β γ -statistical convergence of fuzzy functions of order $$\theta $$ θ

Ojha

Srivastava

2016

J. Appl. Math. Comput.

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Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted αβ -statistical convergence of order θ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigated in terms of their α-cuts. The interrelation among them are also established. We have also proved that continuity, boundedness etc are preserved in the equi-statistical sense under some suitable conditions, but not in pointwise sense.

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Section: Preliminariesmentioning

confidence: 99%

Some characterizations on weighted $$\beta \gamma $$ β γ -statistical convergence of fuzzy functions of order $$\theta $$ θ

Ojha

Srivastava

2016

J. Appl. Math. Comput.

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“…Pointwise statistical convergence sequences of fuzzy mappings studied by Altin et al [17]. Some beneficial results on this topic can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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

Kı̇şı̇

2021

Journal of Mathematics

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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.

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“…Para estudios realizados sobre números difusos, los teoremas de Tauberian con vistas a Cesáro y la sumabilidad estadísstica de Cesáro fueron obtenidos por (Canak, Totur, &Önder, 2017), (Önder, Ç anak, & Totur, 2017) y para la convergencia estadística de (Talo & Bayazit, 2017). (Gong, Zhang, & Zhu, 2015) discutieron sobre la convergencia estadística y otras nociones asociadas para sucesionesúnicas de funciones con valores difusos y también obtuvieron algunas sus propiedades básicas. Recientemente, (Hazarika, Alotaibi, & Mohiuddine, 2020) estudiaron la convergencia estadística en medida sobre doble sucesiones para funciones con valores difusos y obtuvieron algunas propiedades importantes las cuales serán de gran utilidad para el desarrollo de este artículo.…”

Section: Introductionunclassified

Convergencia estadística en medida para sucesiones triples de funciones con valores difusos

Granados¹

2021

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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En este artículo, definimos y extendemos las nociones de dos tipos de convergencia en medida, estos son interna y externa estadística convergencia para sucesiones triples de funciones medibles con valores difusos. Además, mostramos que ambas sucesiones son equivalentes en un espacio de medida finita. Adicionalmente, definimos y estudiamos la noción de estadística convergencia en medida para sucesiones triples de funciones medibles con valores difusos. En adición, mostramos y probamos la versión estadística del teorema de Egorov para sucesiones triples de funciones con valores difusos sobre un espacio de medida finita.

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The statistical convergence for sequences of fuzzy-number-valued functions

Cited by 14 publications

References 15 publications

Some characterizations on weighted $$\beta \gamma $$ β γ -statistical convergence of fuzzy functions of order $$\theta $$ θ

Some characterizations on weighted $$\beta \gamma $$ β γ -statistical convergence of fuzzy functions of order $$\theta $$ θ

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

Convergencia estadística en medida para sucesiones triples de funciones con valores difusos

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