Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Uniqueness of Single Peak Solutions for a Kirchhoff Equation
Mathematics 2024, 12(10), 1462; https://doi.org/10.3390/math12101462 (registering DOI) - 8 May 2024
Abstract
We deal with the following singular perturbation Kirchhoff equation:
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We deal with the following singular perturbation Kirchhoff equation: where constants and . In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on asymptotic behaviors of and its first derivatives by using a type of Pohozaev identity for a small enough . To some extent, our result exhibits a new phenomenon for a kind of which allows for different orders in different directions.
Full article
(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
Modeling, Analysis and Evaluation of a Novel Compact 6-DoF 3-RRRS Needle Biopsy Robot
by
Jiangnan Wang, Ruiqi Xiang, Jindong Xiang, Baichuan Wang, Xiyun Wu, Mingzhen Cai, Zhijie Pan, Mengtang Li and Xun Li
Mathematics 2024, 12(10), 1461; https://doi.org/10.3390/math12101461 - 8 May 2024
Abstract
Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed
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Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed designed for specific application scenarios, and only position-level kinematics are derived, preventing advanced speed control or singularity analysis. As a step forward, this paper aims to design a universal needle biopsy robot platform which features 6 DoF 3-RRRS (Revolute–Revolute–Revolute–Spherical) parallel structure. The analytical solutions to its nonlinear kinematic problems, including forward kinematics, inverse kinematics, and differential kinematics are derived, allowing fast and accurate feedback control calculations. A multibody simulation platform and a first-generation prototype are established next to provide comprehensive verifications for the derived robotic model. Finally, simulated puncture experiments are carried out to illustrate the effectiveness of the proposed method.
Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
Open AccessArticle
Fixed Point Results for Compatible Mappings in Extended Parametric Sb-Metric Spaces
by
Sunil Beniwal, Naveen Mani, Rahul Shukla and Amit Sharma
Mathematics 2024, 12(10), 1460; https://doi.org/10.3390/math12101460 - 8 May 2024
Abstract
This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal
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This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations.
Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
Open AccessArticle
A Dynamic Hierarchical Improved Tyrannosaurus Optimization Algorithm with Hybrid Topology Structure
by
Shihong Zhang, Hu Shi, Baizhong Wang, Chunlu Ma and Qinghua Li
Mathematics 2024, 12(10), 1459; https://doi.org/10.3390/math12101459 - 8 May 2024
Abstract
Aiming at the problems of the Tyrannosaurus optimization algorithm, of poor search accuracy, insufficient global search capability, and ease of falling into local optimality, a dynamic hierarchical improved Tyrannosaurus optimization algorithm (DHTROA) with hybrid topology structure is proposed. Initially, a chaotic opposition-based learning
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Aiming at the problems of the Tyrannosaurus optimization algorithm, of poor search accuracy, insufficient global search capability, and ease of falling into local optimality, a dynamic hierarchical improved Tyrannosaurus optimization algorithm (DHTROA) with hybrid topology structure is proposed. Initially, a chaotic opposition-based learning approach is selected to start the population, ensuring a more uniform distribution of prey across the solution area and boosting population diversity; later, a dynamic hybrid bi-population strategy is introduced to divide the initial population into an ‘advantaged group’ and a ‘disadvantaged group’ to improve the efficiency of individual information exchange. Finally, the ‘advantaged group’ and ‘disadvantaged group’ are hunted synchronously; for the ‘advantaged group’, the position update is carried out using the cellular ring topology strategy, and for the ‘disadvantaged group’, the original algorithm is run in accordance with the main loop process. For the problem of the constant running rate of the Tyrannosaurus in the original algorithm, an adaptive running rate strategy is proposed, which enhances the ability of global optimization, and at the same time, the shortcomings of the original algorithm’s ‘failure’ strategy are improved in order to enhance the original algorithm to jump out of extrema. DHTROA was tested for performance with nine optimization algorithms in different dimensions of the CEC2017 test function. The efficiency of these enhancements was confirmed through the Wilcoxon rank sum test and Friedman test, while DHTROA was utilized for six engineering optimization challenges of differing complexities. The experimental results show that DHTROA has improved greatly in convergence speed, optimality search accuracy, global search ability, and stability, and the excellent engineering optimization performance also proves the excellent robustness of DHTROA.
Full article
Open AccessArticle
Backstepping and Novel Sliding Mode Trajectory Tracking Controller for Wheeled Mobile Robots
by
Hangjie Huang and Jinfeng Gao
Mathematics 2024, 12(10), 1458; https://doi.org/10.3390/math12101458 - 8 May 2024
Abstract
A novel variable structure controller based on sliding mode is developed for addressing the trajectory tracking challenge encountered by wheeled mobile robots. Firstly, the trajectory tracking error model under the global coordinate system is established according to the kinematic model of the wheeled
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A novel variable structure controller based on sliding mode is developed for addressing the trajectory tracking challenge encountered by wheeled mobile robots. Firstly, the trajectory tracking error model under the global coordinate system is established according to the kinematic model of the wheeled mobile robot. Secondly, the novel sliding mode algorithm and backstepping method are introduced to design the motion controller of the system, respectively. Different sliding mode surfaces are formulated to guarantee rapid and stable convergence of the system’s trajectory tracking error to zero. Ultimately, comparative simulation trials validate the controller’s ability to swiftly and consistently follow the reference trajectory. In contrast to traditional controllers, this controller shows rapid convergence, minimal error, and robustness.
Full article
(This article belongs to the Special Issue Modeling and Simulation in Engineering, 3rd Edition)
Open AccessArticle
Incorporating the Third Law of Geography with Spatial Attention Module–Convolutional Neural Network–Transformer for Fine-Grained Non-Stationary Air Quality Predictive Learning
by
Shaofu Lin, Yuying Zhang, Xiliang Liu, Qiang Mei, Xiaoying Zhi and Xingjia Fei
Mathematics 2024, 12(10), 1457; https://doi.org/10.3390/math12101457 - 8 May 2024
Abstract
Accurate air quality prediction is paramount in safeguarding public health and addressing air pollution control. However, previous studies often ignore the geographic similarity among different monitoring stations and face challenges in dynamically capturing different spatial–temporal relationships between stations. To address this, an air
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Accurate air quality prediction is paramount in safeguarding public health and addressing air pollution control. However, previous studies often ignore the geographic similarity among different monitoring stations and face challenges in dynamically capturing different spatial–temporal relationships between stations. To address this, an air quality predictive learning approach incorporating the Third Law of Geography with SAM–CNN–Transformer is proposed. Firstly, the Third Law of Geography is incorporated to fully consider the geographical similarity among stations via a variogram and spatial clustering. Subsequently, a spatial–temporal attention convolutional network that combines the spatial attention module (SAM) with the convolutional neural network (CNN) and Transformer is designed. The SAM is employed to extract spatial–temporal features from the input data. The CNN is utilized to capture local information and relationships among each input feature. The Transformer is applied to capture time dependencies across long-distance time series. Finally, Shapley’s analysis is employed to interpret the model factors. Numerous experiments with two typical air pollutants (PM2.5, PM10) in Haikou City show that the proposed approach has better comprehensive performance than baseline models. The proposed approach offers an effective and practical methodology for fine-grained non-stationary air quality predictive learning.
Full article
Open AccessArticle
On Aspects of Continuous Approximation of Diatomic Lattice
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Igor V. Andrianov, Lelya A. Khajiyeva, Askar K. Kudaibergenov and Galina A. Starushenko
Mathematics 2024, 12(10), 1456; https://doi.org/10.3390/math12101456 - 8 May 2024
Abstract
This paper is devoted to the continualization of a diatomic lattice, taking into account natural intervals of wavenumber changes. Continualization refers to the replacement of the original pseudo-differential equations by a system of PDEs that provides a good approximation of the dispersion relations.
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This paper is devoted to the continualization of a diatomic lattice, taking into account natural intervals of wavenumber changes. Continualization refers to the replacement of the original pseudo-differential equations by a system of PDEs that provides a good approximation of the dispersion relations. In this regard, the Padé approximants based on the conditions for matching the values of the dispersion relations of the discrete and continuous models at several characteristic points are utilized. As a result, a sixth-order unconditionally stable system with modified inertia is obtained. Appropriate boundary conditions are formulated. The obtained continuous approximation accurately describes the amplitude ratios of neighboring masses. It is also shown that the resulting continuous system provides a good approximation for the natural frequencies.
Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
Open AccessArticle
Novel Feature-Based Difficulty Prediction Method for Mathematics Items Using XGBoost-Based SHAP Model
by
Xifan Yi, Jianing Sun and Xiaopeng Wu
Mathematics 2024, 12(10), 1455; https://doi.org/10.3390/math12101455 - 8 May 2024
Abstract
The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of
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The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China’s Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the “black box” nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students’ learning needs, thus effectively informing educational practice.
Full article
Open AccessArticle
Absolute Value Inequality SVM for the PU Learning Problem
by
Yongjia Yuan and Fusheng Bai
Mathematics 2024, 12(10), 1454; https://doi.org/10.3390/math12101454 - 8 May 2024
Abstract
Positive and unlabeled learning (PU learning) is a significant binary classification task in machine learning; it focuses on training accurate classifiers using positive data and unlabeled data. Most of the works in this area are based on a two-step strategy: the first step
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Positive and unlabeled learning (PU learning) is a significant binary classification task in machine learning; it focuses on training accurate classifiers using positive data and unlabeled data. Most of the works in this area are based on a two-step strategy: the first step is to identify reliable negative examples from unlabeled examples, and the second step is to construct the classifiers based on the positive examples and the identified reliable negative examples using supervised learning methods. However, these methods always underutilize the remaining unlabeled data, which limits the performance of PU learning. Furthermore, many methods require the iterative solution of the formulated quadratic programming problems to obtain the final classifier, resulting in a large computational cost. In this paper, we propose a new method called the absolute value inequality support vector machine, which applies the concept of eccentricity to select reliable negative examples from unlabeled data and then constructs a classifier based on the positive examples, the selected negative examples, and the remaining unlabeled data. In addition, we apply a hyperparameter optimization technique to automatically search and select the optimal parameter values in the proposed algorithm. Numerical experimental results on ten real-world datasets demonstrate that our method is better than the other three benchmark algorithms.
Full article
(This article belongs to the Special Issue Advances of Machine Learning and Data Mining Using Mathematical Optimization in Honor of the 65th Birthday of Prof. Adil M. Bagirov)
Open AccessArticle
Computation of the Mann–Whitney Effect under Parametric Survival Copula Models
by
Kosuke Nakazono, Yu-Cheng Lin, Gen-Yih Liao, Ryuji Uozumi and Takeshi Emura
Mathematics 2024, 12(10), 1453; https://doi.org/10.3390/math12101453 - 8 May 2024
Abstract
The Mann–Whitney effect is a measure for comparing survival distributions between two groups. The Mann–Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence
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The Mann–Whitney effect is a measure for comparing survival distributions between two groups. The Mann–Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann–Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent of each other, the traditional formula of the Mann–Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann–Whitney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands . Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.
Full article
(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data)
Open AccessArticle
Mathematical Model of the Process of Data Transmission over the Radio Channel of Cyber-Physical Systems
by
Fazliddin Makhmudov, Andrey Privalov, Alexander Privalov, Elena Kazakevich, Gamzatdin Bekbaev, Alexey Boldinov, Kyung Hoon Kim and Young Im-Cho
Mathematics 2024, 12(10), 1452; https://doi.org/10.3390/math12101452 - 8 May 2024
Abstract
This article introduces a refined mathematical model to evaluate the quality of mobile radio channels within cyber-physical systems, employing the topological transformation of stochastic networks. The operation of the radio channel is conceptualized as a stochastic network, enabling the derivation of critical metrics
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This article introduces a refined mathematical model to evaluate the quality of mobile radio channels within cyber-physical systems, employing the topological transformation of stochastic networks. The operation of the radio channel is conceptualized as a stochastic network, enabling the derivation of critical metrics such as an equivalent function, mathematical expectation, variance, and the time distribution function of the implemented processes. The model uses the Gamma distribution for the initial distribution functions of random variables, enhancing its analytical precision. A significant advancement of this study is the development of a comprehensive model that describes the data transmission process through phases of connection establishment, information transmission, and connection maintenance. The innovative aspect of this research lies in applying an equivalent function to a stochastic network that includes a logical “AND” node with gamma-distributed incoming branches. The stochastic network presented in the article, which includes a logical “AND” node, helps to elucidate the mechanism for obtaining an equivalent function for such networks, allowing the application area of the GERT method to be expanded. This methodological enhancement extends the previously limited scope of topological transformation methods, which only applied to exponential distribution models for the timing of branch inputs. By integrating a Gamma distribution, the model simplifies the equivalent function and reduces the computational complexity required to assess the radio channel’s quality, ensuring the accuracy needed for engineering calculations. Moreover, the proposed method requires 25–40% fewer series members than the traditional Taylor series decomposition, while maintaining comparable computational complexity for the typical series members. Furthermore, the maximum absolute error in the calculations is capped at 9 × 10−3, which is well within acceptable limits for engineering purposes. Primarily designed for radio channels in cyber-physical systems, the model’s applicability extends to wireless communications, providing a valuable tool for evaluating channel efficiency and security in the face of increasing cyber threats.
Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security toward Industry 5.0)
Open AccessArticle
Robust Control Based on Adaptative Fuzzy Control of Double-Star Permanent Synchronous Motor Supplied by PWM Inverters for Electric Propulsion of Ships
by
Djamel Ziane, Samir Zeghlache, Mohamed Fouad Benkhoris and Ali Djerioui
Mathematics 2024, 12(10), 1451; https://doi.org/10.3390/math12101451 - 8 May 2024
Abstract
This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially,
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This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially, a modeling technique employing a matrix transformation method is introduced, generating decoupled and independent star windings to eliminate inductive couplings, while maintaining model consistency and torque control. The precise DSPMSM model serves as the foundation for an unknown nonlinear backstepping controller, approximated directly using an adaptive fuzzy controller. Through the Lyapunov direct method, system stability is demonstrated. All signals in the closed-loop system are ensured to be uniformly ultimately bounded (UUB). The proposed control system aims for low tracking errors, while also mitigating the impact of parametric uncertainties. The effectiveness of the adaptive fuzzy nonlinear control system is validated through tests conducted in hardware-in-the-loop (HIL) simulations, utilizing the OPAL-RT platform, OP4510.
Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 2nd Edition)
Open AccessArticle
A Reliable and Privacy-Preserving Vehicular Energy Trading Scheme Using Decentralized Identifiers
by
Myeonghyun Kim, Kisung Park and Youngho Park
Mathematics 2024, 12(10), 1450; https://doi.org/10.3390/math12101450 - 8 May 2024
Abstract
As the usage of electric vehicles (EVs) expands, various energy management technologies, including battery energy storage systems, are being developed to efficiently charge EVs using various energy sources. In recent years, many blockchain-based energy trading schemes have been proposed for secure energy trading.
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As the usage of electric vehicles (EVs) expands, various energy management technologies, including battery energy storage systems, are being developed to efficiently charge EVs using various energy sources. In recent years, many blockchain-based energy trading schemes have been proposed for secure energy trading. However, existing schemes cannot fully solve privacy issues and security problems during energy trading. In this paper, we propose a reliable and privacy-preserving vehicular energy trading scheme utilizing decentralized identifier technology. In the proposed scheme, identity information and trading result information are not revealed publicly; this is due to the use of decentralized identifiers and verifiable credential technologies. Additionally, only parties who have successfully conducted energy trading can manage complete transaction information. We also demonstrate our method’s security and ensure privacy preservation by performing informal and formal security analyses. Furthermore, we analyze the performance and security features of the proposed scheme and related works and show that the proposed scheme has competitive performance.
Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security toward Industry 5.0)
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Open AccessArticle
Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems
by
Tsvetelin Stefanov Zaevski
Mathematics 2024, 12(10), 1449; https://doi.org/10.3390/math12101449 - 8 May 2024
Abstract
The aim of this paper is to examine some American-style financial instruments that lead to two-sided optimal hitting problems. We pay particular attention to derivatives that are similar to strangle options but have a quadratic payoff function. We consider these derivatives in light
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The aim of this paper is to examine some American-style financial instruments that lead to two-sided optimal hitting problems. We pay particular attention to derivatives that are similar to strangle options but have a quadratic payoff function. We consider these derivatives in light of much more general payoff structures under certain conditions which guarantee that the optimal strategy is an exit from a strip. Closed-form formulas for the optimal boundaries and the fair price are derived when the contract has no maturity constraints. We obtain the form of the optimal boundaries under the finite maturity horizon and approximate them by maximizing the financial utility of the derivative holder. The Crank–Nicolson finite difference method is applied to the pricing problem. The importance of these novel financial instruments is supported by several features that are very useful for financial practice. They combine the characteristics of the power options and the ordinary American straddles. Quadratic strangles are suitable for investors who need to hedge strongly, far from the strike positions. In contrast, the near-the-money positions offer a relatively lower payoff than the ordinary straddles. Note that the usual options pay exactly the overprice; no more, no less. In addition, the quadratic strangles allow investors to hedge the positions below and above the strike together. This is very useful in periods of high volatility when large market movements are expected but their direction is unknown.
Full article
(This article belongs to the Section Financial Mathematics)
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Open AccessFeature PaperArticle
Vector Equilibrium Problems—A Unified Approach and Applications
by
Cristina Stamate
Mathematics 2024, 12(10), 1448; https://doi.org/10.3390/math12101448 - 8 May 2024
Abstract
We present existing results and properties for the solutions of some vector equilibrium problems with set-valued functions in the case of a vector space ordered by a cone with some “interiority” properties. Some applications concerning the existence of equilibrium for abstract economies and
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We present existing results and properties for the solutions of some vector equilibrium problems with set-valued functions in the case of a vector space ordered by a cone with some “interiority” properties. Some applications concerning the existence of equilibrium for abstract economies and vector optimization problems are given.
Full article
(This article belongs to the Special Issue Set-Valued Analysis, 3rd Edition)
Open AccessArticle
Key Vulnerable Nodes Discovery Based on Bayesian Attack Subgraphs and Improved Fuzzy C-Means Clustering
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Yuhua Xu, Yang Liu, Zhixin Sun, Yucheng Xue, Weiliang Liao, Chenlei Liu and Zhe Sun
Mathematics 2024, 12(10), 1447; https://doi.org/10.3390/math12101447 - 8 May 2024
Abstract
Aiming at the problem that the search efficiency of key vulnerable nodes in large-scale networks is not high and the consideration factors are not comprehensive enough, in order to improve the time and space efficiency of search and the accuracy of results, a
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Aiming at the problem that the search efficiency of key vulnerable nodes in large-scale networks is not high and the consideration factors are not comprehensive enough, in order to improve the time and space efficiency of search and the accuracy of results, a key vulnerable node discovery method based on Bayesian attack subgraphs and improved fuzzy C-means clustering is proposed. Firstly, the attack graph is divided into Bayesian attack subgraphs, and the analysis results of the complete attack graph are quickly obtained by aggregating the information of the attack path analysis in the subgraph to improve the time and space efficiency. Then, the actual threat features of the vulnerability nodes are extracted from the analysis results, and the threat features of the vulnerability itself in the common vulnerability scoring standard are considered to form the clustering features together. Next, the optimal number of clusters is adaptively adjusted according to the variance idea, and fuzzy clustering is performed based on the extracted clustering features. Finally, the key vulnerable nodes are determined by setting the feature priority. Experiments show that the proposed method can optimize the time and space efficiency of analysis, and the fuzzy clustering considering multiple features can improve the accuracy of analysis results.
Full article
(This article belongs to the Special Issue Fuzzy Modeling and Fuzzy Control Systems)
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Open AccessFeature PaperArticle
Fuzzy Evaluation Model for Products with Multifunctional Quality Characteristics: Case Study on Eco-Friendly Yarn
by
Kuen-Suan Chen, Tsun-Hung Huang, Kuo-Ching Chiou and Wen-Yang Kao
Mathematics 2024, 12(10), 1446; https://doi.org/10.3390/math12101446 - 8 May 2024
Abstract
Numerous advanced industrial countries emphasize green environmental protection alongside athletic healthcare. Many world-renowned sports brands are actively developing highly functional, environmentally friendly, and aesthetically pleasing products. For example, in the production of sports shoes, the eco-friendly yarn process is one of the important
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Numerous advanced industrial countries emphasize green environmental protection alongside athletic healthcare. Many world-renowned sports brands are actively developing highly functional, environmentally friendly, and aesthetically pleasing products. For example, in the production of sports shoes, the eco-friendly yarn process is one of the important processes. This process involves multiple crucial larger-the-better quality characteristics closely tied to the functionality of sports shoes. Facing green environmental regulations and external competitors, it is evidently an imperative issue for enterprises to consider how to improve the quality of newly developed products, increase product value, and lower rates of both rework and scrap to accomplish the goals of saving energy and minimizing waste. Aiming to solve this problem, this study proposed a fuzzy evaluation model for products with multifunctional quality characteristics to assist the sporting goods manufacturing industry in evaluating whether all functional quality characteristics of its products meet the required quality level. This study first utilized the larger-the-better Six Sigma quality index concerning environmental protection for evaluation and then proposed product evaluation indicators for the eco-friendly yarn. Since the parameters of these indicators have not yet been determined, sample data need to be used for estimation. Enterprises require rapid response, so that the sample size is relatively small. Sampling error will increase the risk of misjudgment. Therefore, taking suggestions from previous studies, this study constructed the fuzzy evaluation model based on confidence intervals of quality indicators for the eco-friendly yarn. This method incorporated previous experience with data, thereby enhancing assessment accuracy.
Full article
(This article belongs to the Special Issue Advances and Applications on Fuzzy Logic for Decision Making Processes)
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Open AccessArticle
Age-Related Macular Degeneration Detection in Retinal Fundus Images by a Deep Convolutional Neural Network
by
Andrés García-Floriano and Elías Ventura-Molina
Mathematics 2024, 12(10), 1445; https://doi.org/10.3390/math12101445 - 8 May 2024
Abstract
Computer-based pre-diagnosis of diseases through medical imaging is a task worked on for many years. The so-called fundus images stand out since they do not have uniform illumination and are highly sensitive to noise. One of the diseases that can be pre-diagnosed through
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Computer-based pre-diagnosis of diseases through medical imaging is a task worked on for many years. The so-called fundus images stand out since they do not have uniform illumination and are highly sensitive to noise. One of the diseases that can be pre-diagnosed through fundus images is age-related macular degeneration, which initially manifests as the appearance of lesions called drusen. Several ways of pre-diagnosing macular degeneration have been proposed, methods based entirely on the segmentation of drusen with prior image processing have been designed and applied, and methods based on image pre-processing and subsequent conversion to feature vectors, or patterns, to be classified by a Machine-Learning model have also been developed. Finally, in recent years, the use of Deep-Learning models, particularly Convolutional Networks, has been proposed and used in classification problems where the data are only images. The latter has allowed the so-called transfer learning, which consists of using the learning achieved in the solution of one problem to solve another. In this paper, we propose the use of transfer learning through the Xception Deep Convolutional Neural Network to detect age-related macular degeneration in fundus images. The performance of the Xception model was compared against six other state-of-the-art models with a dataset created from images available in public and private datasets, which were divided into training/validation and test; with the training/validation set, the training was made using 10-fold cross-validation. The results show that the Xception neural network obtained a validation accuracy that surpasses other models, such as the VGG-16 or VGG-19 networks, and had an accuracy higher than 80% in the test set. We consider that the contributions of this work include the use of a Convolutional Neural Network model for the detection of age-related macular degeneration through the classification of fundus images in those affected by AMD (drusen) and the images of healthy patients. The performance of this model is compared against other methods featured in the state-of-the-art approaches, and the best model is tested on a test set outside the training and validation set.
Full article
(This article belongs to the Special Issue Application of Artificial Intelligence, Machine Learning and Data Science in Industrial and Medical Domains)
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Open AccessArticle
A Novel Hybrid Gray MCDM Model for Resilient Supplier Selection Problem
by
Alptekin Ulutaş, Mladen Krstić, Ayşe Topal, Leonardo Agnusdei, Snežana Tadić and Pier Paolo Miglietta
Mathematics 2024, 12(10), 1444; https://doi.org/10.3390/math12101444 - 8 May 2024
Abstract
The current business climate has generated considerable uncertainty and disrupted supply chain processes. Suppliers have frequently been identified as the primary source of hazards responsible for supply chain disruptions. Using a strategic approach to supplier selection that prioritizes providers with resilience features, mitigating
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The current business climate has generated considerable uncertainty and disrupted supply chain processes. Suppliers have frequently been identified as the primary source of hazards responsible for supply chain disruptions. Using a strategic approach to supplier selection that prioritizes providers with resilience features, mitigating the risk exposure inherent in supply chains is possible. This study proposes a comprehensive gray multiple-criteria decision making (MCDM) method incorporating resilience attributes to supplier selection. To determine criteria weights, the gray PSI and gray BWM methodologies were used, and to evaluate and prioritize resilient providers, the gray MCRAT and gray COBRA methodologies were applied. According to the results obtained by the suggested methodology, the supplier that demonstrated the greatest degree of resilience was determined to be the provider categorized as SPIR 4. The sequential sequence of the SPIR numbers is as follows: SPIR 5, SPIR 1, SPIR 3, SPIR 2, and SPIR 6. The data demonstrate that the developed approach produced accurate results.
Full article
(This article belongs to the Special Issue Multi-criteria Optimization Models and Methods for Smart Cities)
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Open AccessArticle
The Operational Laws of Symmetric Triangular Z-Numbers
by
Hui Li, Xuefei Liao, Zhen Li, Lei Pan, Meng Yuan and Ke Qin
Mathematics 2024, 12(10), 1443; https://doi.org/10.3390/math12101443 - 8 May 2024
Abstract
To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension
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To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers.
Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Systems)
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