On the convergence of uncertain random sequences

Ahmadzade, Hamed; Sheng, Yuhong; Esfahani, Mojtaba

doi:10.1007/s10700-016-9242-z

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…Meanwhile, the definitions, properties and principles of cross-entropy (Chen et al, 2012 ; Gao et al, 2018 ), triangular entropy (Ning et al, 2015 ), partial entropy (Ahmadzade et al, 2017a ), sine entropy (Yao et al, 2013a ), quadratic entropy (Dai, 2018 ), maximum entropy (Chen & Dai, 2011 ), and relative entropy (Zhou et al, 2015 , 2016 ; Sheng et al, 2017b ) have been proposed in several papers. Furthermore, the convergence concept of uncertain sequences and their interrelation (You, 2009 ; Wu & Xia, 2012 ; Chen et al, 2014 , 2016 ; Ahmadzade et al, 2017b ), and the limit theorem (Wang et al, 2018 , 2018 ), have also been discussed in many publications.…”

Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

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Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

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Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

show abstract

“…In order to describe this phenomenon, Liu [33] first proposed the chance theory, which is a mathematical methodology for modeling complex systems with both uncertainty and randomness. Regarding the theoretical aspect, Ahmadzade et al [1] studied some properties of uncertain random sequences. As an application of chance theory, Liu [34] proposed the uncertain random programming as a branch of mathematical programming involving uncertain random variables.…”

Section: Chance Theorymentioning

confidence: 99%

Cycle index of uncertain random graph

Chen

Peng

Rao

et al. 2018

IFS

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Abstract. With the increasing of the complexity of a system, there is a variety of indeterminacy in the practical applications of graph theory. We focus on uncertain random graph, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. In this paper, the chance theory is applied to construct the cycle index of an uncertain random graph. Then a method to calculate the cycle index of an uncertain random graph is presented. We also discuss some properties of the cycle index.

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“…In order to study the convergence theorems of uncertain random sequences, Ahmadzade et al [2] introduced the following concepts of convergence: It is mentioned that for ξ = τ n + iη n and ξ = τ + iη, ||ξ n − ξ|| is computed as follows:…”

Section: Uncertain Random Variablementioning

confidence: 99%

“…Furthermore, as major device in chance theory, Liu [17] presented operational law of uncertain random variables. After that, several scholars devoted their studies to applications of uncertain random variables, for instance Guo and Wang [9], Gao et al [5], Ahmadzade et al [1,2], Gao and Sheng [6], Liu and Ralescu [18], and Gao and Yao [8]. For modeling complex quantities in chance theory, Gao et al [7] introduced the concept of complex uncertain random variables.…”

Section: Introductionmentioning

confidence: 99%