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In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures.

The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams ‘fairness’. These are critical for a large multi-teacher course wherein the teachers are changed such that the course and examination content are altered every few years. However, a fair test with randomly participating students should still be a guaranteed subject with no item pool. Through data-driven decision-making, this study collected data related to a term test for a compulsory general course for empirical assessments, pre-processed the data and used item response theory to statistically estimate the difficulty, discrimination and lower asymptotic for each item in the two exam papers. Binary goal programing was finally used to analyze and balance the fairness of A/B exams without an item pool. As a result, pairs of associated questions in the two exam papers were optimized in terms of their overall balance in three dimensions (as the goals) through the paired exchanges of items. These exam papers guarantee their consistency (in the tested knowledge points) and also ensure the fairness of the term test (a key psychological factor that motivates continued studies). Such an application is novel as the teacher(s) did not have a pre-set question bank and could formulate the fairest strategy for the A/B exam papers. The model can be employed to address similar teaching practice issues.

This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate.

This work presents an optimization proposal to better the computational convergence time in convection-diffusion and driven-cavity problems by applying a simulated annealing (SA) metaheuristic, obtaining optimal values in relaxation factors (RF) that optimize the problem convergence during its numerical execution. These relaxation factors are tested in numerical models to accelerate their computational convergence in a shorter time. The experimental results show that the relaxation factors obtained by the SA algorithm improve the computational time of the problem convergence regardless of user experience in the initial low-quality RF proposal.

Carbon asset management has become an important way to reduce carbon costs. There are three main carbon asset management modes, including carbon quota compliance, carbon asset autonomous management, and custody. A key challenge faced by capital-constrained enterprises is how to scientifically select a carbon asset management mode based on actual needs. This paper considers the impacts of setup costs of carbon asset management departments, carbon asset appreciation, custody costs, and revenue sharing, maximizes the enterprises’ profits, develops optimization models for three modes, and provides the optimal low-carbon production strategies. This paper provides evidence for enterprises to choose optimal modes under different capital levels and carbon emissions by comparing modes. The conclusions are as follows. When setup costs are low, the carbon asset autonomous management mode is suggested for the optimal profit. With higher setup costs, either carbon asset compliance or custody mode is recommended. Under abundant capital, the carbon asset custody mode is suggested. Given a certain amount of capital and low setup costs, high-emission enterprises are encouraged to adopt the carbon asset autonomous management mode for a win–win of profits and carbon emissions. The carbon asset custody and compliance modes are suggested for medium-emission and low-emission enterprises, respectively.

This paper examines the use of algorithms and non-algorithmic models in mathematics and science, especially in biology, during the past century by summarizing the gradual development of a conceptual rationale for non-algorithmic models in biology. First, beginning a century ago, mathematicians found it impossible to constrain mathematics in an algorithmic straitjacket via öö’s Incompleteness Theorems, so how would it be possible in biology? By the 1930s, biology was resolutely imitating classical physics, with biologists enforcing a reductionist agenda to expunge function, purpose, teleology, and vitalism from biology. Interestingly, physicists and mathematicians often understood better than biologists that mathematical representations of living systems required different approaches than those of dead matter. Nicolas Rashevsky, the Father of Mathematical Biology, and Robert Rosen, his student, pointed out that the complex systems of life cannot be reduced to machines or mechanisms as per the Newtonian paradigm. Robert Rosen concluded that living systems are not amenable to algorithmic models that are primarily syntactical. Life requires semantics for its description. Rashevsky and Rosen pioneered Relational Biology, initially using Graph Theory to model living systems. Later, Rosen created a metabolic–repair model (M, R)-system using Category Theory to encode the basic entailments of life itself. Although reductionism still dominates in current biology, several subsequent authors have built upon the Rashevsky–Rosen intellectual foundation and have explained, extended, and explored its ramifications. Algorithmic formulations have become increasingly inadequate for investigating and modeling living systems. Biology is shifting from a science of simple systems to complex ones. This transition will only be successful once mathematics fully depicts what it means to be alive. This paper is a call to mathematicians from biologists asking for help in doing this.

The knapsack problem is a typical bi-objective combinatorial optimization issue, wherein maximizing the value of the packed items is achieved concurrently with minimizing the weight of the load. Due to the conflicting objectives of the knapsack problem and the typical discrete property of the items involved, swarm intelligence algorithms are commonly employed. The diversity of optimal combinations in the knapsack problem has become a focal point, which involves finding multiple packing solutions at the same value and weight. For this purpose, this paper proposes a Multi-Objective Equilibrium Optimizer Algorithm based on Weighted Congestion Distance (MOEO_WCD). The algorithm employs a non-dominated sorting method to find a set of Pareto front solutions rather than a single optimal solution, offering multiple decision-making options based on the varying needs of the decision-makers. Additionally, MOEO_WCD improves the balance pool generation mechanism and incorporates a weighted congestion incentive, emphasizing the diversity of packing combination solutions under the objectives of value and weight to explore more Pareto front solutions. Considering the discrete characteristics of the knapsack combination optimization problem, our algorithm also incorporates appropriate discrete constraint handling. This paper designs multiple sets of multi-objective knapsack combinatorial optimization problems based on the number of knapsacks, the number of items, and the weights and values of the items. This article compares five algorithms suitable for solving multi-objective problems: MODE, MO-PSO-MM, MO-Ring-PSO-SCD, NSGA-II, and DN-NSGAII. In order to evaluate the performance of the algorithm, this paper proposes a new solution set coverage index for evaluation. We also used the hypervolume indicator to evaluate the diversity of algorithms. The results show that our MOEO-WCD algorithm achieves optimal coverage of the reference composite Pareto front in the decision space of four knapsack problems. The experimental results indicate that our MOEO_WCD algorithm achieves the optimal coverage of the reference composite Pareto front in the decision space for four sets of knapsack problems. Although our MOEO_WCD algorithm covers less of the composite front in the objective space compared with the MODE algorithm for knapsack problem 1, its coverage of the integrated reference solutions in the decision space is greater than that of the MODE algorithm. The experiments demonstrate the superior performance of the MOEO_WCD algorithm on bi-objective knapsack combinatorial optimization problem instances, which provides an important solution to the search for diversity in multi-objective combinatorial optimization solutions.

This paper studies the properties of the evolution operators of a class of time-delay systems with linear delayed dynamics. The considered delayed dynamics may, in general, be time-varying and associated with a finite set of finite constant point delays. Three evolution operators are defined and characterized. The basic evolution operator is the so-called point delay operator, which generates the solution trajectory under point initial conditions at t0=0. Furthermore, this paper also considers the whole evolution operator and the delay strip evolution operator, which define the solution trajectory, respectively, at any time instant and along a strip of time whose size is that of the maximum delay. These operators are defined for any given bounded piecewise continuous function of initial conditions on an initialization time interval of measure being identical to the maximum delay. It is seen that the semigroup property of the time-invariant undelayed dynamics, which is generated by a C0-semigroup, becomes lost by the above evolution operators in the presence of the delayed dynamics. This fact means that the point evolution operator is not a strongly and uniformly continuous one-parameter semigroup, even if its undelayed part has a time-invariant associated dynamics. The boundedness and the stability properties of the time-delay system, as well as the strong and uniform continuity properties of the evolution operators, are also discussed.

In this paper, the optimal control problem of hydrocarbons’ hydrogenation was investigated in the presence of two catalysts—Nickel–Kieselguhr and Raney Nickel. This multistage chemical reaction holds significant practical importance, particularly in the production of high-density fuels. The optimal control problem was reformulated as a nonlinear global optimization problem and addressed using a modified Mind Evolutionary Computation algorithm. The proposed modifications include methods designed to ensure solution feasibility and ease of practical implementation. Using the proposed method, the performance of the two catalysts was compared under constant temperature conditions and with optimal control strategies. The results demonstrate that selecting an effective catalyst has a greater impact on the reaction’s efficiency than temperature control alone, with the Raney Nickel catalyst consistently outperforming the Nickel–Kieselguhr catalyst by at least 17%. Additionally, the optimization approach was applied to identify a new set of catalyst parameters. The newly obtained catalyst parameters allowed for the improvement of the results of the Raney Nickel catalyst by 18%. The results of all numerical experiments and implementation details are described in the paper.

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.

In reinforcement learning, off-policy temporal difference learning methods have gained significant attention due to their flexibility in utilizing existing data. However, traditional off-policy temporal difference methods often suffer from poor convergence and stability when handling complex problems. To address these issues, this paper proposes an off-policy temporal difference algorithm with Bellman residuals (TDBR). By incorporating Bellman residuals, the proposed algorithm effectively improves the convergence and stability of the off-policy learning process. This paper first introduces the basic concepts of reinforcement learning and value function approximation, highlighting the importance of Bellman residuals in off-policy learning. Then, the theoretical foundation and implementation details of the TDBR algorithm are described in detail. Experimental results in multiple benchmark environments demonstrate that the TDBR algorithm significantly outperforms traditional methods in terms of both convergence speed and solution quality. Overall, the TDBR algorithm provides an effective and stable solution for off-policy reinforcement learning with broad application prospects. Future research can further optimize the algorithm parameters and extend its application to continuous state and action spaces to enhance its applicability and performance in real-world problems.

Autism is a challenging brain disorder affecting children at global and national scales. Applied behavior analysis is commonly conducted as an efficient medical therapy for children. This paper focused on one paradigm of applied behavior analysis, imitation, where children mimic certain lessons to enhance children’s social behavior and play skills. This paper introduces IMITASD, a practical monitoring assessment model designed to evaluate autistic children’s behaviors efficiently. The proposed model provides an efficient solution for clinics and homes equipped with mid-specification computers attached to webcams. IMITASD automates the scoring of autistic children’s videos while they imitate a series of lessons. The model integrates two core modules: attention estimation and imitation assessment. The attention module monitors the child’s position by tracking the child’s face and determining the head pose. The imitation module extracts a set of crucial key points from both the child’s head and arms to measure the similarity with a reference imitation lesson using dynamic time warping. The model was validated using a refined dataset of 268 videos collected from 11 Egyptian autistic children during conducting six imitation lessons. The analysis demonstrated that IMITASD provides fast scoring, takes less than three seconds, and shows a robust measure as it has a high correlation with scores given by medical therapists, about 0.9, highlighting its effectiveness for children’s training applications.

This paper presents a novel method for fabricating three-dimensional (3D) microstructures of cobalt–platinum (Co-Pt) permanent magnets using a localized electrochemical deposition (LECD) technique. The method involves the use of an electrolyte and a micro-nozzle to control the deposition process. However, traditional methods face significant challenges in controlling the thickness and uniformity of deposition layers, particularly in the manufacturing of magnetic materials. To address these challenges, this paper proposes a method that integrates machine learning algorithms to optimize the electrochemical deposition parameters, achieving a Co:Pt atomic ratio of 50:50. This optimized ratio is crucial for enhancing the material’s magnetic properties. The Co-Pt microstructures fabricated exhibit high coercivity and remanence magnetization comparable to those of bulk Co-Pt magnets. Our machine learning framework provides a robust approach for optimizing complex material synthesis processes, enhancing control over deposition conditions, and achieving superior material properties. This method opens up new possibilities for the fabrication of 3D microstructures with complex shapes and structures, which could be useful in a variety of applications, including micro-electromechanical systems (MEMSs), micro-robots, and data storage devices.

In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making.

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs.

No matter whether with constraint or without constraint, most of the research about distributed optimization is studied for the kind of quadratic performance criteria that does not have an integrator; these optimization problems only concern the state value at the time of the final state, not the whole process of the system change. For this problem, this paper discusses second-order multi-agent systems with a discrete-time dynamic and a continuous-time dynamic, respectively, for distributed optimization control problems, and proposes sufficient conditions to ensure the quadratic performance criteria with an integrator is positive. Specifically, under sufficient conditions, we describe the multi-agent systems that are considered in this paper to be connected topology; all the agents can obtain the information from their neighbors. In addition, the structure of our controller only relies on the Laplace matrix of the system’s topology, and the reaction coefficients in the controller are the parameters in the performance criteria. Finally, the analysis of convergence is given and verified by numerical examples and simulations.

The development of innovative materials, based on the modern technologies and processes, is the key factor to improve the energetic sustainability and reduce the environmental impact of electrical equipment. In particular, the modeling of magnetic hysteresis is crucial for the design and construction of electrical and electronic devices. In recent years, additive manufacturing techniques are playing a decisive role in the project and production of magnetic elements and circuits for applications in various engineering fields. To this aim, the use of the deep learning paradigm, integrated with the most common models of the magnetic hysteresis process, has become increasingly present in recent years. The intent of this paper is to provide the features of a wide range of deep learning tools to be applied to magnetic hysteresis context and beyond. The possibilities of building neural networks in hybrid form are innumerable, so it is not plausible to illustrate them in a single paper, but in the present context, several neural networks used in the scientific literature, integrated with various hysteretic mathematical models, including the well-known Preisach model, are compared. It is shown that this hybrid approach not only improves the modeling of hysteresis by significantly reducing computational time and efforts, but also offers new perspectives for the analysis and prediction of the behavior of magnetic materials, with significant implications for the production of advanced devices.

COVID-19 is an enveloped virus with a single-stranded RNA genome. The surface of the virus contains spike proteins, which enable the virus to attach to host cells and enter the interior of the cells. After entering the cell, the virus exploits the host cell’s mechanisms for replication and dissemination. Since the end of 2019, COVID-19 has spread rapidly around the world, leading to a large-scale epidemic. In response to the COVID-19 pandemic, the global scientific community quickly launched vaccine research and development. Vaccination is regarded as a crucial strategy for controlling viral transmission and mitigating severe cases. In this paper, we propose a novel mathematical model for COVID-19 infection incorporating vaccine-induced immunization failure. As a cornerstone of infectious disease prevention measures, vaccination stands as the most effective and efficient strategy for curtailing disease transmission. Nevertheless, even with vaccination, the occurrence of vaccine immunization failure is not uncommon. This necessitates a comprehensive understanding and consideration of vaccine effectiveness in epidemiological models and public health strategies. In this paper, the basic regeneration number is calculated by the next generation matrix method, and the local and global asymptotic stability of disease-free equilibrium point and endemic equilibrium point are proven by methods such as the Routh–Hurwitz criterion and Lyapunov functions. Additionally, we conduct fractional-order numerical simulations to verify that order 0.86 provides the best fit with COVID-19 data. This study sheds light on the roles of immunization failure and fractional-order control.

The aim of this research is to minimize the number of container-rehandling operations in both the yard and on the ship in order to solve the problem of coordinated optimization of ship loading and yard container retrieval and enhance the loading efficiency of automated container terminals,. An optimization model that integrates the optimized decision-making of both the container retrieval order from the yard and the ship’s space allocation is developed, and an improved cuckoo algorithm is employed to solve the optimization problem. This paper examines the influence of container retrieval order from the yard on rehandling within the yard, as well as the effect of the ship’s space allocation on subsequent rehandling operations at the unloading port. Experimental results demonstrate that the solution derived from the comprehensive optimization model based on the improved cuckoo algorithm considerably reduces the overall number of overturned containers. This confirms that the proposed optimization model effectively enhances loading efficiency and reduces container rehandling both in the yard and on the ship. The analysis of experimental results indicates that the model and algorithm proposed in this paper have certain applicability.

In recent years, China’s financial markets have come under increasing scrutiny. In order to explore the impact of financial literacy on urban household investment in the risk financial market, this paper used the micro-data of the 2019 China Household Finance Survey (CHFS) to start from two perspectives: household risk financial investment and the number of investment financial products, namely the breadth of investment. By constructing a probit model and ordered probit model for empirical analysis, the main conclusions are as follows. Benchmark regression results show that the improvement of financial literacy can significantly promote urban households to make risky financial investments and can significantly broaden the types of risky financial investments. Based on the IV-probit model and two-stage least square method, the endogeneity test using the economic and financial information attention degree as the instrumental variable showed that the model results were credible. The robustness test showed that the model results were basically correct. Furthermore, the mechanism analysis found that the use of fintech played an intermediary effect in the process of financial literacy affecting urban household risky financial investment and the amount of investment. This indicates that the improvement of financial literacy can improve the probability of using fintech, thus promoting the household risky financial investment behavior. Heterogeneity analysis based on risk attitude showed that financial literacy had a greater effect on the improvement in the risky financial investment behavior of risk-inclined families, followed by risk-neutral families, and had the least effect on risk-averse families. The research conclusions of this paper are of practical significance to solve the problems related to urban household financial market investment. Therefore, this paper puts forward some suggestions for reference, especially in terms of financial education and the digital economy.

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to parameters have not been thoroughly studied. In this paper, we make an attempt to fill this gap. Our results are not complete; for some functions, we manage to establish (log)-convexity/concavity in parameters, while for others, we only managed the prove monotonicity, in which case we present necessary and sufficient conditions for convexity/concavity. In the course of the investigation, we found two hypergeometric representations for the generalized cosine and hyperbolic cosine functions which appear to be new. In the last section of the paper, we present four explicit integral evaluations of combinations of generalized trigonometric/hyperbolic functions in terms of hypergeometric functions.

This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications.

Prime Power RSA is a variant of the RSA scheme due to Takagi with modulus N=prq for r⩾2, where p,q are of the same bit-size. In this paper, we concentrate on one type of Prime Power RSA which assumes e·d≡1modpr−1(p−1)(q−1). Two new attacks on this type of Prime Power RSA are presented when given two pairs of public and private exponents, namely, (e1,d1) and (e2,d2) with the same modulus N. Suppose that d1

The fuel economy of electric vehicles (EVs) is an important factor in determining the competitiveness of EVs. Since the fuel economy is affected by the efficiency of an e-powertrain composed of a motor and inverter, it is necessary to select a high-efficiency topology for the e-powertrain. In this paper, a novel topology of e-powertrains to improve the fuel economy of EVs is proposed. The proposed topology aims to improve the system efficiency by integrating open-end winding (OEW) and winding changeover (WC). The proposed OEW-PMSM with WC enables to drive a permanent magnet synchronous motor (PMSM) in four different modes. Each mode can increase inverter efficiency and motor efficiency by changing motor parameters and maximum modulation index. In this paper, the system efficiency of the proposed topology was evaluated using electromagnetic finite element analysis and a loss model of power semiconductors. In addition, the vehicle simulations were performed to evaluate the fuel economy of the proposed topology, thereby proving the superiority of the proposed topology compared with the conventional PMSM.

Production rescheduling involves re-optimizing production schedules in response to disruptions that render the initial schedule inefficient or unfeasible. This process requires simultaneous consideration of multiple objectives to develop new schedules that are both efficient and stable. However, existing review papers have paid limited attention to the multi-objective optimization techniques employed in this context. To address this gap, this paper presents a systematic literature review on multi-objective production rescheduling, examining diverse shop-floor environments. Adhering to the PRISMA guidelines, a total of 291 papers were identified. From this pool, studies meeting the inclusion criteria were selected and analyzed to provide a comprehensive overview of the problems tackled, dynamic events managed, objectives considered, and optimization approaches discussed in the literature. This review highlights the primary multi-objective optimization methods used in relation to rescheduling strategies and the dynamic disruptive events studied. Findings reveal a growing interest in this research area, with “a priori” and “a posteriori” optimization methods being the most commonly implemented and a notable rise in the use of the latter. Hybridized algorithms have shown superior performance compared to standalone algorithms by leveraging combined strengths and mitigating individual weaknesses. Additionally, “interactive” and “Pareto pruning” methods, as well as the consideration of human factors in flexible production systems, remain under-explored.

In this paper, we investigate the relationships among point transitivity, topological transitivity, Li–Yorke chaos, and the existence of irregular vectors for a linear semiflow {Tt}t∈Δ indexed with a complex sector. We reveal the equivalence between topological transitivity and point transitivity for a linear semiflow {Tt}t∈Δ, especially in case the range of some operator Tt,t∈Δ is not dense. We also prove that Li–Yorke chaos is equivalent to the existence of a semi-irregular vector and that point transitivity is stronger than the existence of an irregular vector for any linear semiflow Ttt∈Δ. At last, unlike the conclusion for traditional linear dynamical systems, we show that there exists a Li–Yorke chaotic C0-semigroup Ttt∈Δ without irregular vectors. The results and proof methods presented in this paper demonstrate the differences in the dynamical behavior between linear semiflows {Tt}t∈Δ and traditional linear systems with the acting semigroup S=Z+ and S=R+.

Dynamic simulation is widely applied in the real-time and realistic physical simulation field. How to achieve natural dynamic simulation results in real-time with small data sizes is an important and long-standing topic. In this paper, we propose a dynamic reconstruction and interpolation method grounded in physical principles for simulating dynamic deformations. This method replaces the deformation forces of the widely used eXtended Position-Based Dynamics (XPBD), which are traditionally derived from the gradient of the energy potential defined by the constraint function, with the elastic beam bending forces to more accurately represent the underlying deformation physics. By doing so, it establishes a mathematical model based on dynamic partial differential equations (PDE) for reconstruction, which are the differential equations involving both the parametric variable u and the time variable t. This model also considers the inertia forces caused by acceleration. The analytical solution to this model is then integrated with the XPBD framework, built upon Newton’s equations of motion. This integration reduces the number of design variables and data sizes, enhances simulation efficiency, achieves good reconstruction accuracy, and makes deformation simulation more capable. The experiment carried out in this paper demonstrates that deformed shapes at about half of the keyframes simulated by XPBD can be reconstructed by the proposed PDE-based dynamic reconstruction algorithm quickly and accurately with a compact and analytical representation, which outperforms static B-spline-based representation and interpolation, greatly shortens the XPBD simulation time, and represents deformed shapes with much smaller data sizes while maintaining good accuracy. Furthermore, the proposed PDE-based dynamic reconstruction algorithm can generate continuous deformation shapes, which cannot be generated by XPBD, to raise the capacity of deformation simulation.

In September 2024, the Fashion-MNIST dataset will be 7 years old. Proposed as a replacement for the well-known MNIST dataset, it continues to be used to evaluate machine learning model architectures. This paper describes new results achieved with the Fashion-MNIST dataset using classical machine learning models and a relatively simple convolutional network. We present the state-of-the-art results obtained using the CNN-3-128 convolutional network and data augmentation. The developed CNN-3-128 model containing three convolutional layers achieved an accuracy of 99.65% in the Fashion-MNIST test image set. In addition, this paper presents the results of computational experiments demonstrating the dependence between the number of adjustable parameters of the convolutional network and the maximum acceptable classification quality, which allows us to optimise the computational cost of model training.

Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov’s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

Solar irradiance prediction is a crucial component in the application of photovoltaic power generation, playing a vital role in optimizing energy production, managing energy storage, and maintaining grid stability. This paper proposes an irradiance prediction method based on a functionally structured inverted transformer network, which maintains the channel independence of each feature in the model input and extracts the correlations between different features through an Attention mechanism, enabling the model to effectively capture the relevant information between various features. After the channel mixing of different features is completed through the Attention mechanism, a linear network is used to predict the irradiance sequence. A data processing method tailored to the prediction model used in this paper is designed, which employs a comprehensive data preprocessing approach combining mutual information, multiple imputation, and median filtering to optimize the raw dataset, enhancing the overall stability and accuracy of the prediction project. Additionally, a Dingo optimization algorithm suitable for the self-tuning of deep learning model hyperparameters is designed, improving the model’s generalization capability and reducing deployment costs. The artificial intelligence (AI) model proposed in this paper demonstrates superior prediction performance compared to existing common prediction models in irradiance data forecasting and can facilitate further applications of photovoltaic power generation in power systems.

This paper focuses on the pricing problem of binary options under stochastic interest rates, stochastic volatility, and a mixed exponential jump diffusion model. Considering the negative interest rates in the market in recent years, this paper assumes that the stochastic interest rate follows the Hull–White (HW) model. In addition, we assume that the stochastic volatility follows the Heston volatility model, and the price of the underlying asset follows the jump diffusion model in which the jumps follow the mixed exponential jump model. Considering these factors comprehensively, the mixed exponential jump diffusion of the Heston–HW (abbreviated as MEJ-Heston–HW) model is established. Using the idea of measure transformation, the pricing formula of binary call options is derived by the martingale method, eigenfunction, and Fourier transform. Finally, the effects of the volatility term and the parameters of the mixed-exponential jump diffusion model on the option price in the O-U process are analyzed. In the numerical simulation, compared with the double exponential jump Heston–HW (abbreviated as DEJ-Heston–HW) model and the Heston–HW model, the mixed exponential jump model is an extension of the double exponential jump model, which can approximate any distribution in the sense of weak convergence, including arbitrary discrete distributions, normal distributions, and various thick-tailed distributions. Therefore, the MEJ-Heston–HW model adopted in this paper can better describe the price of the underlying asset.

In this paper, an extendable fuzzy robust speed controller suitable for induction motor drive systems was proposed. Firstly, the two-degrees-of-freedom (2DOF) robust control technology with feedforward control and disturbance elimination method was adopted. Upon parameter variation and load disturbance, the motor drive system could utilize a robust controller to generate compensation signals and reduce the impact on the controlling performance of the motor drive system. The magnitude of the compensation signal was adjusted via the weighting factor. However, should a fixed weighting factor be adopted, system instability might be generated easily when time delay and saturation of control force occur. Based on the above, the smart method of extendable fuzzy theory (EFT) was adopted in this paper to adjust adequate weighting factors, where the controlling performance of the induction motor drive system could be improved accordingly. Lastly, the simulation software Matlab/Simulink (R2023b version) was applied to simulate the utilization of the controlling method proposed for the induction motor drive system. The simulation results proved that the extendable fuzzy robust speed controller proposed provided better speed tracking and load regulation-controlling performance than the conventional robust controller.

With the rapid development of smart grids, the strategic behavior evolution in user-side electricity market transactions has become increasingly complex. To explore the dynamic evolution mechanisms in this area, this paper systematically reviews the application of evolutionary game theory in user-side electricity markets, focusing on its unique advantages in modeling multi-agent interactions and dynamic strategy optimization. While evolutionary game theory excels in explaining the formation of long-term stable strategies, it faces limitations when dealing with real-time dynamic changes and high-dimensional state spaces. Thus, this paper further investigates the integration of deep reinforcement learning, particularly the deep Q-learning network (DQN), with evolutionary game theory, aiming to enhance its adaptability in electricity market applications. The introduction of the DQN enables market participants to perform adaptive strategy optimization in rapidly changing environments, thereby more effectively responding to supply–demand fluctuations in electricity markets. Through simulations based on a multi-agent model, this study reveals the dynamic characteristics of strategy evolution under different market conditions, highlighting the changing interaction patterns among participants in complex market environments. In summary, this comprehensive review not only demonstrates the broad applicability of evolutionary game theory in user-side electricity markets but also extends its potential in real-time decision making through the integration of modern algorithms, providing new theoretical foundations and practical insights for future market optimization and policy formulation.

The purpose of this paper is to show how the self-exciting threshold autoregressive (SETAR) model might be a suitable econometric framework for characterizing the dynamics of the US public debt/GDP ratio after the Bretton Woods collapse. Our preferred SETAR specifications are capable of capturing the main stylized facts of the US public debt/GDP ratio between 1974 and 2024. In addition, the estimated SETAR models are consistent with theoretical frameworks that look to explain the behavior of the US public debt/GDP ratio before and after the Global Financial Crisis (GFC). Finally, under the assumption of public debt/GDP ratio stationarity, for which we find only limited and inconclusive evidence, this paper provides some arguments for why previous studies, which use the exponential smooth threshold autoregressive (ESTAR) models, logistic smooth threshold autoregressive (LSTAR) models or SETAR-type models for the first differences of the US public debt/GDP ratio, are potentially misspecified on both econometric and economic grounds.

In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with a remainder depending on the types of remainder. We also prove several important theorems on the asymptotic representation of integrals of Karamata functions. Under certain conditions, we observe a “narrowing” of classes of slowly varying functions concerning the types of remainder. At the end of the paper, we discuss the possibilities of the application of slowly varying functions in the theory of stochastic branching systems. In particular, under the condition of the finiteness of the moment of the type Exlnx for the particle transformation intensity, it is established that the property of slow variation with a remainder is implicitly present in the asymptotic structure of a non-critical Markov branching random system.

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, orientations of twists and the formation of pointed based space under a homeomorphic continuous function. It is shown that the Dehn twisted homotopy under non-retraction admits a left lifting property (LLP) through the local homeomorphism. The LLP extends the principles of Hurewicz fibration by avoiding pullback. Moreover, this paper illustrates that the Dehn twisted homotopy up to a base point in a based space can be formed by considering retraction. As a result, two disjoint continuous functions become point-wise continuous at the base point under retracted homotopy twists. Interestingly, the oriented Dehn twists of a pre-twisted space under homotopy retraction mutually commute in a contractible space.

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently.

Nonlinear control theory applied to unmanned aeronautical vehicles is an engineering topic that has received higher and higher popularity during the last decade. Model-based control approaches have shown increased performance in flight control accuracy and robustness compared to model-free proposals based on parameter adaptation and estimation. However, model-based structures need more computational efforts in terms of spatial and temporal variables. To avoid these constraints, the latest drone flight controls are based on quaternion models, ensuring more advanced computational performances. To this aim, this paper deals with a flight control algorithm of a quadrotor, in which the mathematics model of the plant is defined in terms of quaternions. Additionally, when aerial vehicles are used in specific applications such as slung load transportation and agriculture fields, among others, the variation of the mass receives high importance since it could make the entire system unstable. In the same line of ideas, this paper presents a H∞ strategy, combined with a Super-Twisting Sliding-Mode Control, ensuring the control objective of the mass variations identification, and trajectory tracking, to be solved. The stability analysis of the proposed control approach is also discussed, and the quality and performances of the presented control strategy are tested by simulations, in an interesting case in which mass variations and external perturbations cannot be negligible.

Surface blending is an important topic in geometric modelling and is widely applied in computer-aided design and creative industries to create smooth transition surfaces. Among various surface blending methods, partial differential equation (PDE)-based surface blending has the advantages of effective shape control and exact satisfaction of blending boundary constraints. However, it is not easy to solve partial differential equations subjected to blending boundary constraints. In this paper, we investigate how to solve PDEs analytically and develop an analytical PDE-based method to achieve surface blending with C2 continuity. Taking advantage of elementary functions identified from blending boundary constraints, our proposed method first changes blending boundary constraints into a linear combination of the identified elementary functions. Accordingly, the functions for blending surfaces are constructed from these elementary functions, which transform sixth-order partial differential equations for C2 surface blending into sixth-order ordinary differential equations (ODEs). We investigate the analytical solutions of the transformed sixth-order ordinary differential equations subjected to corresponding blending boundary constraints. With the developed analytical PDE-based method, we solve C2 continuous surface blending problems. The surface blending example presented in this paper indicates that the developed method is simple and easy to use. It can be used to effectively control the shape of blending surfaces and at the same time exactly satisfy C2 continuous blending boundary constraints.

The determination of the capital structure is a critical component of a company’s financial decision-making process. The question of how to optimize a firm’s capital structure to increase its value has been a significant topic of interest within the financial community. The employee stock ownership plan (ESOP) has developed rapidly in China’s capital market over the past decade, providing a suitable context for studying the impact of employee equity incentives on capital structure decisions. This paper employs cross-sectional ordinary least squares regression models and unbalanced panel fixed effect models to investigate the impact of employee stock ownership plans (ESOPs) on firms’ capital structure decisions. The analysis is conducted on a sample of Chinese A-share listed companies on the Shanghai and Shenzhen Stock Exchanges. The research considers both static capital structure choice and dynamic capital structure adjustment. We find that the implementation of an ESOP reduces the level of corporate debt and accelerates the dynamic adjustment of capital structure, suggesting that employee equity incentives play a role in optimizing firms’ capital structure decisions. We also find that the impact of ESOPs on the dynamic adjustment of capital structure is asymmetric. Specifically, the implementation of ESOPs markedly accelerates the downward adjustment of capital structure, yet has no impact on the upward adjustment of capital structure. Further analysis demonstrates that the impact of ESOPs on capital structure decisions is contingent upon the macroeconomic environment, industry characteristics, corporate governance, and ESOP contract designs. First, the optimization of ESOPs on capital structure decisions is more pronounced in an economic boom environment, in a poor market climate, or in competitive industries. Second, the reduction effect of ESOPs on corporate debt is more pronounced in non-state-owned companies, high-tech companies and those with lower ownership concentration. In contrast, the acceleration effect of ESOPs on capital structure adjustment is more pronounced in state-owned companies, non-high-tech companies and those with higher ownership concentration. Ultimately, ESOPs financed by loans from a firm’s major shareholders—or with a longer lock-up period, smaller shareholding size or executive subscription ratio—demonstrate a more pronounced optimization effect on capital structure decisions. This paper not only contributes to the existing literature on the relationship between equity incentives and capital structure decisions, but also provides guidance for listed companies on the reasonable design of their ESOPs and the optimization of their capital structure decisions.

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3≤b≤3. These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7≤b<2 are reported together with segments with AP changes (1.7≤b<2.3). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b¯=1.98 (σ=0.3), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony.

In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices.

Satellites adopt a single-task observation mode in traditional patterns. Although this mode boasts high imaging accuracy, it is accompanied by a limited number of observed tasks and a low utilization rate of satellite resources. This limitation becomes particularly pronounced when dealing with extensive and densely populated observation task sets because the inherent mobility of satellites often leads to conflicts among numerous tasks. To address this issue, this paper introduces a novel multi-task merging mechanism aimed at enhancing the observation rate of satellites by resolving task conflicts. Initially, this paper presents a task merging method based on the proposed multitask merging mechanism, referred to as the constrained graph (CG) task merging approach. This method can merge tasks while adhering to the minimal requirements specified by users. Subsequently, a multi-satellite merging scheduling model is established based on the combined task set. Considering the satellite combined-task scheduling problem (SCTSP), an enhanced fireworks algorithm (EFWA) is proposed that incorporates the CG task synthesis mechanism. This algorithm incorporates local search strategies and a population disturbance mechanism to enhance both the solution quality and convergence speed. Finally, the efficacy of the CG algorithm was validated through a multitude of simulation experiments. Moreover, the effectiveness of the EFWA is confirmed via extensive comparisons with other algorithms, including the basic ant colony optimization (ACO) algorithm, enhanced ant colony optimization (EACO) algorithm, fireworks algorithm (FWA), and EFWA. When the number of tasks in the observation area are dense, such as in the case where the number of tasks is 700, the CG + EFWA (CG is adopted in the task merging stage and EFWA is adopted in the satellite combined-task scheduling stage) method improves observation benefits by 70.35% (compared to CG + EACO, CG is adopted in the task merging stage and EACO is adopted in the satellite combined-task scheduling stage), 78.93% (compared to MS + EFWA, MS is adopted in the task merging stage and EFWA is adopted in the satellite combined-task scheduling stage), and 39.03% (compared to MS + EACO, MS is adopted in the task merging stage and EACO is adopted in the satellite combined-task scheduling stage).

This study leverages explainable artificial intelligence (XAI) techniques to analyze public sentiment towards Environmental, Social, and Governance (ESG) factors, climate change, and green finance. It does so by developing a novel multi-task learning framework combining aspect-based sentiment analysis, co-reference resolution, and contrastive learning to extract nuanced insights from a large corpus of social media data. Our approach integrates state-of-the-art models, including the SenticNet API, for sentiment analysis and implements multiple XAI methods such as LIME, SHAP, and Permutation Importance to enhance interpretability. Results reveal predominantly positive sentiment towards environmental topics, with notable variations across ESG categories. The contrastive learning visualization demonstrates clear sentiment clustering while highlighting areas of uncertainty. This research contributes to the field by providing an interpretable, trustworthy AI system for ESG sentiment analysis, offering valuable insights for policymakers and business stakeholders navigating the complex landscape of sustainable finance and climate action. The methodology proposed in this paper advances the current state of AI in ESG and green finance in several ways. By combining aspect-based sentiment analysis, co-reference resolution, and contrastive learning, our approach provides a more comprehensive understanding of public sentiment towards ESG factors than traditional methods. The integration of multiple XAI techniques (LIME, SHAP, and Permutation Importance) offers a transparent view of the subtlety of the model’s decision-making process, which is crucial for building trust in AI-driven ESG assessments. Our approach enables a more accurate representation of public opinion, essential for informed decision-making in sustainable finance. This paper paves the way for more transparent and explainable AI applications in critical domains like ESG.

The data envelopment analysis (DEA) models have been widely recognized and applied in various fields. However, these models have limitations, such as their inability to globally rank DMUs, the efficiency values are definite numerical values, they are unable to reflect potential efficiency changes, and they fail to adequately reflect the degree of the decision maker’s preference. In order to address these shortcomings, this paper combines possibility theory with self-interest and non-self-interest principles to improve the DEA model to provide a more detailed reflection of the differences between DMUs. First, the self-interest and non-self-interest principles are employed to establish the DEA evaluation model, and the determined numerical efficiency is transformed into efficiency intervals. Second, an attitude function is added to the common possible-degree formula to reflect the decision maker’s preference, and a more reasonable method for solving the attitude function is presented. Finally, the improved possible-degree formula proposed in this paper is used to rank and compare the interval efficiencies. This improved method not only provides more comprehensive ranking information but also better captures the decision maker’s preferences. This model takes preference issues into account and has improved stability and accuracy compared with existing models. The application of the improved model in airlines shows that the model proposed in this paper effectively achieved a full ranking. From a developmental perspective, the efficiency levels of Chinese airlines were generally comparable. Joyair and One Two Three performed poorly, exhibiting significant gaps compared with other airlines.