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Symmetry
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Symmetry Applications in Uncertain Differential Equations
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Symmetry Applications in Uncertain Differential Equations

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 4613

Special Issue Editors

Dr. Anshui Li

E-Mail Website
Guest Editor
School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China
Interests: uncertain statistics; bayesian inference
Dr. Waichon Lio

E-Mail Website
Guest Editor
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: uncertainty theory; mathematical programming
Prof. Dr. Baoding Liu

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Interests: uncertainty theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

An uncertain differential equation is a type of differential equation involving uncertain processes. Nowadays, the study of uncertain differential equations is in a period of rapid development, and it involves fields including finance, optimal control, game theory, accelerated degradation test, birth rate, chemical reaction, crude oil price, drug metabolism, electric circuit, epidemic spread, gas futures price, heat conduction, liquid seepage, population, rumor spread, software reliability, spring vibration, and string vibration. The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results involving their symmetry properties, both from a theoretical and an applied point of view.

The topics of interest for this Special Issue include but are not limited to:

  1. uncertain differential equation;
  2. uncertain statistics;
  3. uncertain programming;
  4. uncertain calculus;
  5. uncertain finance.

Dr. Anshui Li
Dr. Waichon Lio
Prof. Dr. Baoding Liu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • uncertain differential equation
  • uncertain statistics
  • uncertainty theory
  • uncertain finance
  • symmetry
  • uncertain process
  • uncertain renewal process
  • uncertain calculus

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Published Papers (5 papers)

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Research

16 pages, 290 KiB  
Article
Parameter Estimation of Uncertain Moving Average Model Based on Least Squares Principle
by Han Wang and Haiyan Shi
Symmetry 2025, 17(5), 656; https://doi.org/10.3390/sym17050656 - 26 Apr 2025
Viewed by 147
Abstract
The uncertain moving average model is a powerful tool to study the time series in which the data are affected by the previous disturbance terms under uncertain environments. However, the influence of uncertain disturbance terms is often ignored in the relevant statistical inference [...] Read more.
The uncertain moving average model is a powerful tool to study the time series in which the data are affected by the previous disturbance terms under uncertain environments. However, the influence of uncertain disturbance terms is often ignored in the relevant statistical inference studies. In order to solve this problem, this paper constructs a symmetric statistical invariant, normal uncertain variable, by sorting out the uncertain moving average model and combining the uncertain disturbance terms, and then applies the least square principle to the parameter estimation of the symmetric statistical invariant to determine the unknown parameters and uncertain disturbance terms in the uncertain moving average model. In addition, a numerical algorithm is designed to calculate the corresponding estimators, and the problems related to hypothesis testing and forecast are also studied. Finally, a numerical example is given to illustrate the proposed method. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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15 pages, 386 KiB  
Article
Parameter Estimation in Multifactor Uncertain Differential Equation with Symmetry Analysis for Stock Prediction
by Jiashuo Zhang, Tingqing Ye, Xiaoya Xu, Yang Liu and Haoran Zheng
Symmetry 2025, 17(4), 620; https://doi.org/10.3390/sym17040620 - 19 Apr 2025
Viewed by 311
Abstract
Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in [...] Read more.
Multifactor uncertain differential equations (MUDEs) are effective tools to model dynamic systems under multi-source noise. With the widespread use of MUDEs, parameter estimation as the bridge between the observed data and the MUDE becomes increasingly important. Thus, how to estimate unknown parameters in a MUDE under a multi-source noise environment is a challenge. To address this, this paper innovatively proposes a moment method to estimate the unknown parameters in a MUDE and illustrates two numerical examples to show the process of estimating parameters. Furthermore, since the system or environment is complex and constantly changing, the parameters in the MUDE are not constants but time-varying functions in many cases. Therefore, parameter estimation for time-varying functions is another challenge. In order to deal with this, this paper develops a method of parameter estimation for time-varying functions in the MUDE based on the moment method. As an application, this method of parameter estimation for time-varying functions is used to model China Merchants Bank stock. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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14 pages, 4905 KiB  
Article
Uncertain Time Series Analysis for the Confirmed Case of Brucellosis in China
by Shanshan Zhang, Yaxuan Zhang, Waichon Lio and Rui Kang
Symmetry 2024, 16(9), 1160; https://doi.org/10.3390/sym16091160 - 5 Sep 2024
Viewed by 803
Abstract
Brucellosis, as an infectious disease that affects both humans and livestock, poses a serious threat to human health and has a severe impact on economic development. Essentially, brucellosis transmission is a kind of study in biological systems, and the epistemic uncertainty existing in [...] Read more.
Brucellosis, as an infectious disease that affects both humans and livestock, poses a serious threat to human health and has a severe impact on economic development. Essentially, brucellosis transmission is a kind of study in biological systems, and the epistemic uncertainty existing in the data of confirmed brucellosis cases in China is realized as significant uncertainty that needs to be addressed. Therefore, this paper proposes an uncertain time series model to explore the confirmed brucellosis cases in China. Then, some methods based on uncertain statistics and symmetry of the biological system are applied, including order estimation, parameter estimation, residual analysis, uncertain hypothesis test, and forecast. The proposed model is practically applied to the data of confirmed brucellosis cases in China from January 2017 to December 2020, and the results show that the uncertain model fits the observed data better than the probabilistic model due to the frequency instability inherent in the data of confirmed brucellosis cases. Based on the proposed model and statistical method, this paper develops an approach to rapidly forecast the number of confirmed brucellosis cases in small sample scenarios, which can contribute to epidemic control in real application. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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15 pages, 3504 KiB  
Article
Least Squares Estimation of Multifactor Uncertain Differential Equations with Applications to the Stock Market
by Nanxuan Wu and Yang Liu
Symmetry 2024, 16(7), 904; https://doi.org/10.3390/sym16070904 - 16 Jul 2024
Cited by 3 | Viewed by 1323
Abstract
Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, [...] Read more.
Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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15 pages, 362 KiB  
Article
A Symmetric Fourth Party Logistics Routing Problem with Multiple Distributors in Uncertain Random Environments
by Xinyu Gao, Xin Gao and Yang Liu
Symmetry 2024, 16(6), 701; https://doi.org/10.3390/sym16060701 - 6 Jun 2024
Cited by 1 | Viewed by 1025
Abstract
Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In [...] Read more.
Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer’s supply, and distributor’s demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. Full article
(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)
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