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Convergence of complex uncertain sequences

Xiumei Chen, Yufu Ning, Xiao Wang
2016 Journal of Intelligent & Fuzzy Systems  
This paper introduces the convergence concepts of complex uncertain sequences: convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence  ...  Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities.  ...  Acknowledgments This work is supported by Natural Science Foundation of Shandong Province (ZR2014GL002).  ... 
doi:10.3233/ifs-152083 fatcat:5gqo6v7pbrbc5opxbpobpyxzva

Almost convergence of complex uncertain double sequences

Birojit Das, Binod Tripathy, Piyali Debnath, Baby Bhattacharya
2021 Filomat  
In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable.  ...  Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment.  ...  Acknowledgment: The authors thank the reviewers for the careful reading of the article and for their comments.  ... 
doi:10.2298/fil2101061d fatcat:3usvrm4isbhzpmzkiogplxarpa

On the convergence of complex uncertain random sequences

Hamed Ahmadzade, Rong Gao, Habib Naderi
2018 Journal of Intelligent & Fuzzy Systems  
This paper aims at putting forward several types of convergence concepts of complex uncertain random sequences. The relations among convergence concepts are derived by some limit theorems.  ...  In addition, for illustrating of convergence theorems, lots of examples are derived. Finally, a lot of counterexamples about relationships between convergence concepts are stated.  ...  Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No.61573210).  ... 
doi:10.3233/jifs-18080 fatcat:5lgxciobyvfm7pmksu64bwkzbq

$S_{\lambda}(\mathcal{I})$-convergence of complex uncertain sequence

O. Kisi
2019 Matematychni Studii  
Tripathy and Kumar [32] introduced statistical convergence of complex uncertain sequence. Kişi and Güler [27] defined λ-statistically convergence of a sequence of uncertain complex variables.  ...  Zhang [33] proved some theorems on the convergence of a sequence of uncertain complex variables.  ...  taking the limit as n → ∞ on both side of above inequality, we obtain Letting n → ∞, we can obtain {ζ n } λ I -statistically converges in measure to ζ.  ... 
doi:10.15330/ms.51.2.183-194 fatcat:ztsp4babonbgzfmmxalc6dkjra

Statistical convergence of complex uncertain sequences defined by Orlicz function

Pankaj Kumar Nath, Binod Chandra Tripathy
2020 Proyecciones  
Convergence Concepts of Complex Uncertain Sequences Complex uncertain sequence is a sequence of complex uncertain variables indexed by integers.  ...  In this section, we discuss about five convergence concepts of complex uncertain sequence: convergence almost surely(a.s.), convergence in measure, convergence in mean, convergence in distribution and  ...  It follows from above Proposition that if {ζ n } statistically converges uniformly a.s to ζ, then lim n→∞ 1 n |{k ≤ n : lim taking the limit as n → ∞ on both side of above inequality, we obtain By Proposition  ... 
doi:10.22199/issn.0717-6279-2020-02-0019 fatcat:tda33u4pdjevrdslzaw62xdj5a

A Generalized of Sλ-I-Convergence of Complex Uncertain Double Sequences

Carlos Granados
2021 Ingeniería y Ciencia  
In this paper, we introduce the λI2 -statistically convergence sequence concepts which are namely λI2 -statistically convergence almost surely (Sλ(I2) a.s.), λI2 -statistically convergence in measure,  ...  Additionally, decomposition theorems and relationships among them are presented, further, when reciprocal of one theorem is not satisfied, an counterexample is shown to support the result.  ...  Acknowledgements Thankful to respected Referees for their careful reading of the paper and several valuable suggestions which has improved the presentation of the paper.  ... 
doi:10.17230/ingciencia.17.34.3 fatcat:ysmayxkervacljftj2jygu7fqe

Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences

Birojit Das, Binod Tripathy, Piyali Debnath, Baby Bhattacharya
2020 Filomat  
In this paper, we introduce the concept of convergence of complex uncertain series. We initiate matrix transformation of complex uncertain sequence and extend the study via linearity and boundedness.  ...  In this context, we prove Silverman-Toeplitz theorem and Kojima-Schur theorem considering complex uncertain sequences. Finally, we establish some results on co-regular matrices .  ...  Acknowledgement The authors express their sincere thanks to the unanimous reviewer for the careful reading of the article and the valuable constructive comments those improved the presentation of the article  ... 
doi:10.2298/fil2014907d fatcat:eua5kgyzajbttnd3xyh2q5jubu

On strongly almost convergence of doubles equences via complex uncertain variable
On strongly almost convergence of double sequences via complex uncertain variable

J. Nath, B. C. Tripathy, B. Bhattacharya
2022 Problemy Analiza  
The aim of this article is to introduce the characterization of strongly almost convergence in complex uncertain double sequences.  ...  We investigate the concept of strongly almost convergence almost surely, convergence in measure, convergence in mean, convergence in distribution, and convergence uniformly almost surely of complex uncertain  ...  [3] explored the idea of convergence in the complex uncertain sequences using the complex uncertain variable.  ... 
doi:10.15393/j3.art.2022.10450 fatcat:y5sywxpyfjgino4bx7egwiwisy

On statistically convergent complex uncertain sequences

B. Das, P. Debnath, B.C. Tripathy
2022 Karpatsʹkì Matematičnì Publìkacìï  
In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space.  ...  We also initiate statistically Cauchy complex uncertain sequence to prove that a complex uncertain sequence is statistically convergent if and only if it is statistically Cauchy.  ...  A convergent complex uncertain sequence converges statistically with preservation of limit in view of the concept uncertain measure. Proof.  ... 
doi:10.15330/cmp.14.1.135-146 fatcat:2qrqkay3qfcftckd4rlb36uayy

Nörlund and Riesz mean of sequence of complex uncertain variables

Binod Tripathy, Pranab Dowari
2018 Filomat  
Also, we prove results on oscillating sequences of complex uncertain variables.  ...  In this article we have investigated some properties of the Nörlund and Riesz mean of sequences of complex uncertain variables.  ...  Acknowledgement The authors thank the reviewers for their comments and suggestions, those improved the presentation of the article.  ... 
doi:10.2298/fil1808875t fatcat:eocdtcybqfanbi3jc4nhd3enu4

Convergence Properties for Uncertain Sequence

Cuilian You, Lijuan Yan
2017 Mathematical Problems in Engineering  
Since convergence for uncertain sequences plays a very important role in uncertainty theory and applications, we investigated some properties of convergence in measure in this paper.  ...  In addition, some theorems and properties of convergence in p-distance were studied.  ...  Acknowledgments This work was supported by Natural Science Foundation of China, Grant no. 61374184.  ... 
doi:10.1155/2017/6307439 fatcat:irdlvg772zgd3e2dqlolvduwm4

On the convergence of uncertain random sequences

H. Ahmadzade, Y. Sheng, M. Esfahani
2016 Fuzzy Optimization and Decision Making  
A Borel-Cantelli lemma for chance measure is obtained based on the continuity assumption of uncertain measure. Finally, several convergence theorems for uncertain random sequences are established.  ...  In this paper, a useful inequality for central moment of uncertain random variables is proved. Based on this inequality, a convergence theorem for sum of uncertain random variables is derived.  ...  In order to study the properties of uncertain random sequences, we introduce the following concepts of convergence: Definition 11 An uncertain random sequence {ξ n , n ≥ 1} is said to be almost surely  ... 
doi:10.1007/s10700-016-9242-z fatcat:u52vz5pcn5f5dbgmgza5xzmow4

Law of large numbers for uncertain random variables with different chance distributions

Rong Gao, Yuhong Sheng
2016 Journal of Intelligent & Fuzzy Systems  
As a fundamental concept in chance theory, uncertain random variable is an extension of random variable and uncertain variable.  ...  This paper obtains a new law of large numbers for independent uncertain random variables but not necessarily identically distributed.  ...  Since τ 1 , τ 2 , . . . are a sequence of independent uncertain variables and f (x, y) is a continuous function, we know that f (x, τ 1 ), f (x, τ 2 ), . . . are a sequence of independent uncertain variables  ... 
doi:10.3233/ifs-162187 fatcat:saq5kdx7incsdnfduzacuetkc4

Supporting chemical process design under uncertainty

A. Wechsung, J. Oldenburg, J. Yu, A. Polt
2010 Brazilian Journal of Chemical Engineering  
The complexity of typical process models limits intuitive engineering estimates to judge the impact of uncertain parameters on the proposed design.  ...  To facilitate automation, a novel relaxation-based heuristic to differentiate between numerical and physical infeasibility when simulations do not converge is introduced.  ...  Additionally, routines to determine the Hammersley sequence, to transform this uniform sequence to the specified probability distribution of the uncertain parameter, and to control runs in Aspen Plus are  ... 
doi:10.1590/s0104-66322010000300009 fatcat:d2b5laq34zcb7jrdcsot5mk4yu

Top-k Queries Over Uncertain Scores [chapter]

Qing Liu, Debabrota Basu, Talel Abdessalem, Stéphane Bressan
2016 Lecture Notes in Computer Science  
We consider here a model of objects with uncertain scores given as probability distributions and the semantics proposed by the state of the art reference work of Soliman, Hyas and Ben-David.  ...  In this context, ranking of uncertain data becomes a crucial issue. Several data models for uncertain data and several semantics for probabilistic top-k queries have been proposed in the literature.  ...  Crowdsourcing") and is a collaboration between the National University of Singapore and Télécom ParisTech.  ... 
doi:10.1007/978-3-319-48472-3_14 fatcat:epldquofcng7vlzpcy4fwfluce
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