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Mathematics
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Uncertainty Analysis, Decision Making and Optimization
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Uncertainty Analysis, Decision Making and Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 12562

Special Issue Editors

Prof. Dr. Jin Peng

E-Mail Website
Guest Editor
Institute of Uncertain Systems, College of Mathematics & Statistics, Huanggang Normal University, Huanggang 438000, China
Interests: uncertainty analysis; uncertain network optimization; intelligent computing
Prof. Dr. Dan Ralescu

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
Interests: mixed models of uncertainty; statistical decision theory; management of large data sets

Special Issue Information

Dear Colleagues,

Decision making usually takes place under uncertainty. Uncertainty analysis in optimization means studying the problems on how to deal with uncertainty efficiently, which is a crossing field between optimization theory and uncertainty theory. In fact, many realistic optimization problems can be solved in the presence of uncertainty. The aim of this Special Issue is to attract leading researchers in these areas in order to reflect the recent advances in uncertainty analysis and optimization theory, both from a theoretical and an applied point of view. All articles related to uncertainty analysis and optimization are invited to be submitted for this Special Issue.

You are cordially invited to submit papers related to all aspects of uncertainty analysis and optimization, both theoretical and practical. The topics of interest for this Special Issue include (but are not limited to): uncertainty analysis on the background of big data, theoretical foundations of optimization with big data, uncertainty modeling, optimization modeling, multi-criteria optimization, intelligent computing, uncertainty theory, uncertain programming, uncertain graphs and uncertain hypergraphs, uncertain network optimization, uncertain hypernetwork optimization, logistics network optimization, big data analysis, uncertain system analysis, uncertain risk analysis, uncertain reliability analysis, uncertain statistics analysis, complex networks and social networking analysis, uncertain processes, uncertain calculus, uncertain differential equations, uncertain VRP, and so on. 

Prof. Dr. Jin Peng
Prof. Dr. Dan Ralescu
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • decision making
  • uncertainty analysis
  • modeling under uncertainty
  • multi-criteria optimization
  • game theory
  • fuzzy modeling
  • optimal control
  • optimization modeling
  • network optimization
  • intelligent computing
  • big data analysis
  • forecasting
  • strategic management
  • risk analysis and management
  • reliability analysis
  • logistics and supply chain management

Published Papers (6 papers)

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Research

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12 pages, 925 KiB  
Article
Research on the Factors Influencing Tourism Revenue of Shandong Province in China Based on Uncertain Regression Analysis
by Shukun Chen, Yufu Ning, Lihui Wang and Shuai Wang
Mathematics 2023, 11(21), 4490; https://doi.org/10.3390/math11214490 - 30 Oct 2023
Viewed by 1444
Abstract
According to the analysis of historical tourism data, it was found that tourism revenue is influenced by multiple factors, and there exists a linear relationship between these factors and tourism revenue. Therefore, this paper employs a linear regression model to investigate the factors [...] Read more.
According to the analysis of historical tourism data, it was found that tourism revenue is influenced by multiple factors, and there exists a linear relationship between these factors and tourism revenue. Therefore, this paper employs a linear regression model to investigate the factors influencing tourism revenue. However, research on tourism data has found that the disturbance term of the linear regression model is not frequency-stable. This indicates that the disturbance term should be an uncertain variable rather than a random variable. Therefore, this paper adopts an uncertain linear regression analysis model and employs the tourism data of Shandong Province in China from 2011 to 2020 as the sample to investigate the factors influencing tourism revenue. The study provides parameter estimation and residual analysis of the model, as well as predictions and confidence intervals of tourism revenue. Additionally, through an uncertain hypothesis test, it was verified that the adopted model fitted the relevant tourism data well. The results show that factors such as the number of travel agencies, railway length, domestic tourist numbers, and per capita disposable income of urban residents have a significant impact on tourism revenue. Based on the study, recommendations and measures for improving tourism revenue of Shandong Province are proposed. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
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9 pages, 258 KiB  
Article
Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model
by Hongmei Shi, Xingbo Zhang, Yuzhen Gao, Shuai Wang and Yufu Ning
Mathematics 2023, 11(20), 4354; https://doi.org/10.3390/math11204354 - 20 Oct 2023
Cited by 2 | Viewed by 1331
Abstract
In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the [...] Read more.
In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the given data are not random, or when the data are imprecise, and only the range of the data is available, the traditional linear regression method cannot be used. This paper presents an uncertain total least squares estimation method and an uncertain robust total least squares linear regression method based on uncertainty theory and total least squares method. The uncertain total least squares estimation can fully consider errors in the given data and the uncertain robust total least squares linear regression method can effectively eliminate outliers in the data. It is possible to obtain a more reasonable fitting effect with both of these methods, as well as to solve the predicted value and the confidence interval with these two methods. In terms of robust total least squares linear regression estimation, both uncertain total least squares regression estimation and uncertain robust total least squares regression estimation are feasible based on numerical examples. There are more accurate fitting equations and more reliable results with uncertain robust least squares linear regression estimation. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
13 pages, 365 KiB  
Article
Robust H∞ Performance Analysis of Uncertain Large-Scale Networked Systems
by Rongxing Guan and Huabo Liu
Mathematics 2023, 11(15), 3377; https://doi.org/10.3390/math11153377 - 2 Aug 2023
Viewed by 752
Abstract
This paper considers the robust H∞ performance problem of continuous-time uncertain large-scale networked systems (LSNSs). The systems consist of numerous arbitrarily connected subsystems, each of which has different dynamics. Currently it is computationally difficult to manage systems with the existing lumped analysis [...] Read more.
This paper considers the robust H∞ performance problem of continuous-time uncertain large-scale networked systems (LSNSs). The systems consist of numerous arbitrarily connected subsystems, each of which has different dynamics. Currently it is computationally difficult to manage systems with the existing lumped analysis method; therefore, exploiting the structural properties of the systems, sufficient conditions are derived for robust H∞ performance. Based on these results, an analysis condition that depends only on the parameters of each single subsystem is further obtained. Some numerical simulations are proposed to verify the validity and superiority of the developed conditions. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
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19 pages, 4339 KiB  
Article
Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty
by Shengwen Yin, Keliang Jin, Yu Bai, Wei Zhou and Zhonggang Wang
Mathematics 2023, 11(5), 1214; https://doi.org/10.3390/math11051214 - 1 Mar 2023
Viewed by 1233
Abstract
In the Dempster–Shafer evidence theory framework, extremum analysis, which should be repeatedly executed for uncertainty quantification (UQ), produces a heavy computational burden, particularly for a high-dimensional uncertain system with multiple joint focal elements. Although the polynomial surrogate can be used to reduce computational [...] Read more.
In the Dempster–Shafer evidence theory framework, extremum analysis, which should be repeatedly executed for uncertainty quantification (UQ), produces a heavy computational burden, particularly for a high-dimensional uncertain system with multiple joint focal elements. Although the polynomial surrogate can be used to reduce computational expenses, the size of the solution space hampers the efficiency of extremum analysis. To address this, a solution-space-reduction-based evidence theory method (SSR-ETM) is proposed in this paper. The SSR-ETM invests minimal additional time for potentially high-efficiency returns in dealing with epistemic uncertainty. In the SSR-ETM, monotonicity analysis of the polynomial surrogate over the range of evidence variables is first performed. Thereafter, the solution space can be narrowed to a smaller size to accelerate extremum analysis if the surrogate model is at least monotonic in one dimension. Four simple functions and an air spring system with epistemic uncertainty demonstrated the efficacy of the SSR-ETM, indicating an apparent superiority over the conventional method. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
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15 pages, 319 KiB  
Article
Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty
by Mansi Verma, Chuei Yee Chen, Adem Kılıçman, Gafurjan Ibragimov and Fong Peng Lim
Mathematics 2022, 10(19), 3638; https://doi.org/10.3390/math10193638 - 5 Oct 2022
Viewed by 1324
Abstract
Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding the [...] Read more.
Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding the extrema, which have been studied under several differentiability conditions. In this study, we establish the sufficient conditions for the existence of minimizers for fuzzy variational problems under a weaker notion of convexity, namely preinvexity and Buckley–Feuring differentiability. We further discuss their application in a cost minimization problem. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)

Review

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45 pages, 2544 KiB  
Review
Uncertainty Analysis and Optimization Modeling with Application to Supply Chain Management: A Systematic Review
by Lin Chen, Ting Dong, Jin Peng and Dan Ralescu
Mathematics 2023, 11(11), 2530; https://doi.org/10.3390/math11112530 - 31 May 2023
Cited by 19 | Viewed by 5009
Abstract
In recent years, there have been frequent cases of impact on the stable development of supply chain economy caused by uncertain events such as COVID-19 and extreme weather events. The creation, management, and impact coping techniques of the supply chain economy now face [...] Read more.
In recent years, there have been frequent cases of impact on the stable development of supply chain economy caused by uncertain events such as COVID-19 and extreme weather events. The creation, management, and impact coping techniques of the supply chain economy now face wholly novel requirements as a result of the escalating level of global uncertainty. Although a significant literature applies uncertainty analysis and optimization modeling (UAO) to study supply chain management (SCM) under uncertainty, there is a lack of systematic literature review and research classification. Therefore, in this paper, 121 articles published in 44 international academic journals between 2015 and 2022 are extracted from the Web of Science database and reviewed using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). Bibliometric analysis and CiteSpace software are used to identify current developments in the field and to summarize research characteristics and hot topics. The selected published articles are classified and analyzed by author name, year of publication, application area, country, research purposes, modeling methods, research gaps and contributions, research results, and journals to comprehensively review and evaluate the SCM in the application of UAO. We find that UAO is widely used in SCM under uncertainty, especially in the field of decision-making, where it is common practice to abstractly model the decision problem to obtain scientific decision results. This study hopes to provide an important and valuable reference for future research on SCM under uncertainty. Future research could combine uncertainty theory with supply chain management segments (e.g., emergency management, resilience management, and security management), behavioral factors, big data technologies, artificial intelligence, etc. Full article
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
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