Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Special Issues
Symmetry Analysis of Uncertainty Theory and Uncertain Statistics and Their...
share announcement

Symmetry Analysis of Uncertainty Theory and Uncertain Statistics and Their Interdisciplinary Applications

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

Deadline for manuscript submissions: 31 May 2026 | Viewed by 1132

Special Issue Editors

Dr. Yang Liu

E-Mail Website
Guest Editor
School of Science, China University of Geosciences, Beijing 100083, China
Interests: uncertainty theory; uncertain statistics; uncertain differential equation
Dr. Tingqing Ye

E-Mail Website
Guest Editor
School of Science, China University of Geosciences, Beijing 100083, China
Interests: uncertainty theory; uncertain analysis; uncertain statistic
Special Issues, Collections and Topics in MDPI journals
Dr. Waichon Lio

E-Mail Website
Guest Editor
Associate Professor, School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: uncertain theory; uncertain statistics; uncertain production risk processes
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Uncertainty theory is a branch of mathematics relating to the analysis of uncertain phenomena whose frequencies are far from stable, while uncertain statistics constitutes a set of mathematical techniques for collecting, analyzing, and interpreting data by uncertainty theory. Nowadays, the study of uncertainty theory and uncertain statistics is in a period of rapid development, and it involves fields including finance and economics, control and decision-making, engineering, social sciences, physics, biology, and many more. The aim of this Special Issue is to attract leading researchers in these areas to include new high-quality results involving uncertainty theory and uncertain statistics and relevant interdisciplinary applications, both from a theoretical and an applied point of view. The topics of interest for this Special Issue include but are not limited to the following areas:

  • Uncertain statistics;
  • Uncertain differential equation;
  • Uncertain renewal process;
  • Uncertain programming;
  • Uncertain inference control;
  • Uncertain finance.

Dr. Yang Liu
Dr. Tingqing Ye
Dr. Waichon Lio
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 250 words) can be sent to the Editorial Office for assessment.

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 statistics
  • uncertain differential equation
  • uncertain renewal process
  • uncertain programming
  • uncertain inference control
  • uncertain finance
  • symmetric statistical invariant

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

13 pages, 329 KB  
Article
Conservative Hypothesis Test of Multivariate Data from an Uncertain Population with Symmetry Analysis in Music Statistics
by Anshui Li, Jiajia Wang, Shiqi Yao and Wenxing Zeng
Symmetry 2025, 17(11), 1973; https://doi.org/10.3390/sym17111973 - 15 Nov 2025
Viewed by 288
Abstract
Music data exhibits numerous distinct symmetric and asymmetric patterns—ranging from symmetric pitch sequences and rhythmic cycles to asymmetric phrase structures and dynamic shifts. These varied and often subjective patterns present notable challenges for data analysis, such as distinguishing meaningful structural features from noise [...] Read more.
Music data exhibits numerous distinct symmetric and asymmetric patterns—ranging from symmetric pitch sequences and rhythmic cycles to asymmetric phrase structures and dynamic shifts. These varied and often subjective patterns present notable challenges for data analysis, such as distinguishing meaningful structural features from noise and adapting analytical methods to accommodate both regularity and irregularity. To tackle this challenge, we present a novel uncertain hypothesis test, referred to as the conservative hypothesis test, which is designed to assess the validity of statistical hypotheses associated with the symmetric and asymmetric patterns exhibited by two multivariate normal uncertain populations. Specifically, we extend the uncertain hypothesis test for the mean difference between two single-characteristic normal uncertain populations to the multivariate case, filling a research gap in uncertainty theory. Building on this two-population multivariate hypothesis test, we propose the conservative hypothesis test—a feasible uncertain hypothesis testing method for multivariable scenarios, developed based on multiple comparison procedures. To demonstrate the practical utility of these methods, we apply them to music-related statistical data, assessing whether two groups of evaluators use consistent criteria to score music. In essence, the hypothesis tests proposed in this paper hold significant value for social sciences, particularly music statistics, where data inherently contains ambiguity and uncertainty. Full article
(This article belongs to the Special Issue Symmetry Analysis of Uncertainty Theory and Uncertain Statistics and Their Interdisciplinary Applications)
►▼ Show Figures

Figure 1

20 pages, 354 KB  
Article
Residual-Based Improved Uncertain Maximum Likelihood Estimation for Uncertain Delay Differential Equations
by Han Wang, Zhiqiang Zhang and Haiyan Shi
Symmetry 2025, 17(11), 1939; https://doi.org/10.3390/sym17111939 - 12 Nov 2025
Viewed by 177
Abstract
As a powerful tool for characterizing the time-evolution behavior of dynamic systems with delay characteristics, the parameter estimation problem for uncertain delay differential equations has always been a research hotspot in the field of uncertain statistics. In order to eliminate the impact of [...] Read more.
As a powerful tool for characterizing the time-evolution behavior of dynamic systems with delay characteristics, the parameter estimation problem for uncertain delay differential equations has always been a research hotspot in the field of uncertain statistics. In order to eliminate the impact of outliers on the relevant results during parameter estimation, this paper proposes the improved uncertain maximum likelihood estimation and the generalized improved uncertain maximum likelihood estimation for uncertain delay differential equations based on symmetric statistical invariants, named residuals. After that, a numerical algorithm is also designed to solve the numerical solutions of the corresponding estimators. Finally, two numerical examples and an empirical study on stock price modeling are provided to illustrate the effectiveness of the methods proposed in this paper. Full article
(This article belongs to the Special Issue Symmetry Analysis of Uncertainty Theory and Uncertain Statistics and Their Interdisciplinary Applications)
►▼ Show Figures

Figure 1

23 pages, 5145 KB  
Article
Parameter Estimation of General Uncertain Differential Equations via the Principle of Least Squares with Its Application in Economic Field
by Xiaoya Xu and Youde Dong
Symmetry 2025, 17(10), 1594; https://doi.org/10.3390/sym17101594 - 24 Sep 2025
Cited by 1 | Viewed by 403
Abstract
The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view [...] Read more.
The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view of this disadvantage, this paper derives a symmetrical statistical invariant, which is different from residuals based on the difference scheme, and proposes the least squares estimation of general uncertain differential equations based on the statistical invariant and the principle of least squares. In order to consider parameter estimation in more general cases, this paper also studies the least squares estimation of time-varying parameters in general uncertain differential equations and designs corresponding to numerical algorithms to calculate the numerical solutions of these least squares estimations. Finally, this paper also proposes two numerical examples and an empirical study to illustrate the above methods. Full article
(This article belongs to the Special Issue Symmetry Analysis of Uncertainty Theory and Uncertain Statistics and Their Interdisciplinary Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop