This paper investigates the optimal control problems arising within a Stackelberg game framework for public–private pension systems under uncertainty theory. A Stackelberg game model is constructed to derive the optimal control strategies for private pension accounts and government-managed public pension funds, where the government acts as the leader and individuals serve as followers. The dynamic behavior of the system is characterized by uncertain differential equations. By integrating dynamic programming approaches with game theory, the optimal strategies for both sides of the game are derived. Sensitivity analysis reveals that higher public pension contribution rates encourage participants to increase their allocation to risky assets, while a rise in the risk premium reduces their willingness to consume in advance.
This manuscript is concerned with the averaging principle of switched stochastic fuzzy delay differential inclusion by fBm and the Rosenblatt process under the Hilfer fractional derivative. Furthermore, this work aims to enhance fuzzy system theory by integrating stochastic multi-valued systems and switched dynamical models. Under appropriate conditions, the original equation’s mild solution is shown to be approximately equivalent to the corresponding reduced averaged equation’s mild solution. The proposed framework uses switching signals to model transitions among a finite set of subsystems and time-varying structural changes in the dynamics, where each signal uniquely determines the active subsystem at any given time. The investigation is done based on fractional calculus and Cauchy-Schwarz inequality. Also, the required results of the considered model are determined using the stochastic analysis and multivalued analysis. Additionally, numerical section is provided to verify the obtained theoretical results. Furthermore, numerical simulations are given to study the considered model.
This paper introduces a novel approach for generating natural language explanations of SQL queries. To bridge the structural gap between SQL and linear text, we propose injecting the hierarchical information from SQL’s Abstract Syntax Tree (AST) directly into a neural generator. We design structure-encoded trees that decompose a query into its core components (e.g., SELECT clause, conditions). A formal encoding algorithm then assigns each token a structural code representing its precise role and position within the query’s hierarchy. These structural encodings are integrated into a pre-trained Transformer model by replacing BERT’s standard segment embeddings, creating a structure-aware encoder. This modified model is fine-tuned on the WikiSQL dataset to generate fluent descriptions. Experiments demonstrate the effectiveness of our method, achieving a BLEU score of 30.0 and substantially outperforming classical baselines on the SQL-to-text task. The results confirm that explicitly modeling SQL’s inherent hierarchical semantics leads to more accurate and natural-language explanations. Overall, this work presents an effective strategy for incorporating syntactic structural bias into text generation, significantly improving the interpretability and quality of SQL query explanations.
Entity Resolution (ER) is a critical task in data management, where the challenge of imbalanced binary classification frequently arises, leading to significant difficulties in accurately matching records. This study addresses this challenge by introducing a novel approach, the Linear Exponential Loss Function Fuzzy Soft Support Vector Machine (LF-SSVM). The proposed model enhances the traditional Fuzzy Soft SVM by integrating a Linear Exponential (LINEX) loss function, which is specifically designed to handle the complexities associated with imbalanced datasets. The LINEX loss function, recognized for its asymmetric properties, effectively addresses misclassifications by treating them differently based on their characteristics, thereby improving the accuracy of ER in imbalanced scenarios. Additionally, the model is specifically designed to enhance the identification and matching of entities in datasets where certain classes are underrepresented. By utilizing a Primal-Dual optimization method, the model ensures robustness against noisy and imbalanced data while preserving the core structure of the LF-SSVM. Extensive experiments conducted on fifteen real-world ER datasets confirm the effectiveness of our approach, demonstrating substantial improvements over traditional methods in handling imbalanced class distributions in ER tasks.
Uncertainty theory, as a branch of mathematics, provides a modeling framework for uncertain phenomena and has attracted considerable scholarly attention, particularly since 2020. During this period, more than 58
Customer opinions, preferences, and decision-makers’ insights play a vital role in marketing by influencing product development, strategy, and customer experience. Computing with Words (CWW) offers an effective method for processing this qualitative information using linguistic terms instead of numerical values. This work aims to explore the application of one of the most widely used methodologies in CWW—the 2-tuple linguistic model—in marketing. It employs a combination of bibliometric analysis and a systematic literature review for a comprehensive analysis. Articles published between 2000 and 2024 on the Web of Science database are analyzed, incorporating Scopus´s Field-Weighted Citation Impact (FWCI) metrics to assess the impact of individual studies and the average influence of research in marketing-related areas. From an initial sample of 165 peer-reviewed articles, 90 were selected for analysis. The findings indicate that the 2-tuple linguistic model is primarily applied to decision-making problems, with Multiple Attribute Group Decision Making emerging as the most prominent theme due to its high centrality and high density in the strategic diagram, as well as its strong connections to various marketing-related areas. The 2-tuple linguistic model is widely applied in areas such as supplier management and product development and innovation, with digital transformation and consumer behavior representing potential directions for applying the model to address their respective marketing challenges. Using the FWCI, this work also identifies marketing-related areas within decision-making themes where the 2-tuple linguistic model is already applied but has limited influence, revealing opportunities for development and future research.
This paper introduces the triangular fuzzy number (TFN)-valued gamma function and the T-Laplace transform, extending classical analytical operators to the TFN-valued functions. By leveraging a specialized component-wise structure for TFNs, we establish the fundamental properties and theoretical foundations of these transforms through rigorous proofs. The practical utility of the T-Laplace transform is demonstrated by solving fuzzy integro-differential equations within a T-electric circuit model. We demonstrate that for prescribed T-initial conditions, this framework maintains structural consistency throughout the transformation process. This enables the derivation of the TFN-valued analytical solution for the T-current, effectively modeling system uncertainty while preserving the characteristic TFN structure of the output.
A correct definition and understanding of the functions performed by the Compliance Officer are essential for ensuring proper accountability in the nonprofit sector. This study validates the functions assigned to the Compliance Officer through a set of indicators based on the ISO 37301 standard on Compliance Management Systems. These indicators are weighted using the Best–Worst Method (BWM), a multi-criteria decision-making approach that derives their relative importance from expert judgment. Specifically, we apply a fuzzy version of the BWM, which enables the use of consensus-based linguistic assessments and enhances the interpretability and practical treatment of the indicators, thus supporting more accurate accountability processes. For the evaluation, we rely on a panel of experts from Spanish Nonprofit Cooperative Societies. The participation of multiple specialists strengthens the applicability and robustness of the indicators, reduces individual bias, and increases the reliability of the results. Nevertheless, some limitations must be acknowledged, including potential homogeneity in expert profiles and challenges in generalizing the findings to organizations operating under different regulatory environments. This research jointly examines the role of the Compliance Officer and its connection to accountability. Effective accountability is crucial in Nonprofit Cooperative Societies, and the Compliance Officer plays a central role in supporting sound management and everyday operations. Our findings contribute organizational knowledge that can drive innovation in how these entities function, ultimately promoting improved practices in the sector. Well-designed compliance functions not only help prevent sanctions and misinformation but also foster ethics, transparency, and sustainability, which are core pillars of social development.
Uncertain delay differential equations are important mathematical tools for studying the evolution laws of dynamic systems with delay characteristics over time in uncertain environments. However, the current research on the numerical solution methods for this type of equations is still insufficient, and there are also several paradoxes in the related theoretical system that need to be clarified. In order to improve the theoretical and algorithmic research on numerical solutions of uncertain delay differential equations, this paper focuses on a specific form of uncertain delay differential equations and systematically explores the mathematical properties of their α paths and the relevant applications in numerical solutions. Specifically, this paper first provides a complete proof of the continuity and monotonicity of the α paths of the specific form of uncertain delay differential equations with respect to the parameter α . Utilizing these properties, this paper further demonstrates the relationship between the α paths and the solution of the original equation, that is, the α paths are the inverse uncertainty distributions of the corresponding solutions. Based on the above conclusions, this paper finally proposes a numerical algorithm based on the α paths that can be used to solve this type of uncertain delay differential equations.
Uncertainty theory has been verified to effectively address the epistemic uncertainty owing to lack of experience or knowledge. Based on uncertainty theory, we concentrate on the reliability analysis for uncertain wave equation model which is used to describe the propagation of waves. Firstly, we probe into the uncertainty distribution pertaining to the first hitting time of the uncertain wave equation and devised a numerical algorithm aimed at deriving the uncertainty distribution of the first hitting time. Additionally, there is a broad consensus within the academic community that the first hitting time serves as a type of fundamental analytic tool for addressing reliability assessment of dynamic systems. Thus, by using fist hitting time, we propose belief reliability function and belief reliable lifetime for assessing the reliability of uncertain wave equation model. Moreover, for discussing the belief reliability function and belief reliable lifetime, we consider two special cases of the uncertain wave equation model: one is under fixed force and the other is under periodic force. Eventually, we verify the validity of belief reliability function and belief reliable lifetime for uncertain wave equation model by using some examples.
This paper proposes the concept of double quasi-statistical convergence within the framework of credibility theory. Quasi-statistical convergence, as a generalization of statistical convergence, plays a key role in capturing more generalized and intricate patterns of convergence in fuzzy variables. Extending earlier studies, we develop this notion for double sequences and examine its connections with other convergence types in credibility theory, providing new insights into two-dimensional fuzzy systems
This paper deals with the portfolio adjustment problem considering background risk, loss aversion and transaction costs simultaneously in an uncertain environment. Given the complexity of financial markets, situations arise where historical data fail to predict future returns, and expert estimates must be used instead. Based on uncertainty theory, we first establish an uncertain mean-risk index utility model with background risk, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then the effects of changes in the mean of the background asset and the loss aversion coefficient on the optimal utility value are discussed. To reveal the effects of loss aversion and background risk on investment decisions, we present an economic analysis of investment strategies. Our analysis displays that background risk influences not only portfolio selection but also the investor’s effective loss aversion coefficient. The results show that the proposed portfolio model can indirectly express investors’ preferences by the different background asset returns. Furthermore, we provide complete comparative statics analysis and demonstrate the interaction effects between background risk and loss aversion parameters.
This paper introduces an uncertain energy spot price model to characterize the dynamic evolution of electricity and coal prices in markets with limited data availability. By integrating seasonal components and mean-reverting uncertain differential equations, the proposed model effectively captures the non-storage nature and price spikes inherent in energy commodities. Unlike traditional stochastic models reliant on large historical datasets, our framework leverages uncertainty theory to address belief degrees under insufficient observations. The model is further applied to price dark-spread options, which derive value from the spread between electricity and coal spot prices. Numerical experiments using real market data demonstrate the models superior performance over stochastic counterparts in capturing price volatility and generating reliable confidence intervals. This work bridges a critical gap in energy derivatives valuation by providing a robust tool for investors and risk managers operating in data-scarce environments.
In a situation of both cognitive uncertainty and objective randomness, reliability models subject to delayed and instantaneous failures are constructed in this paper. Initially, an uncertain fractional degradation process with memory is introduced, and shocks are modeled as random processes. Considering the system’s physical characteristics and external disturbance, failure thresholds are quantified as variables with two types of indeterminacy. Next, using the proposed belief reliability indexes, reliability formulas in specific cases are derived by chance measures. To ensure that the system performs required functions without failures, periodic maintenance and aging test-based preventive maintenance strategies are adopted. Finally, a numerical example of metal stents is carried out to verify the effectiveness of the proposed methods.
A joint replenishment problem (JRP) considering multiple types of uncertainties and carbon emission cost under a carbon cap-and-trade policy is studied in this paper. In particular, a novel fuzzy JRP is primarily formulated, in which the influences on the budget control arising from uncertainties of product defective rate and fuzzy cost parameters, and the carbon emission during the replenishment are for the first time taken into account simultaneously. Accordingly, a fuzzy dependent-chance programming (DCP) with the aim of maximizing the credibility of budget control is constructed. Following that, improved hybrid intelligent algorithms named BIS-DE and Exact-DE are designed to solve the proposed novel fuzzy JRP efficiently by employing the bisection fuzzy simulation method and the differential evolution algorithm. Furthermore, based on advanced inverse operational laws, the novel fuzzy DCP model is transformed into an equivalent deterministic counterpart which could be solved with the intelligent algorithm without any simulation process. The effectiveness and superiority of both treatments for the novel fuzzy JRP are illustrated by performing numerical experiments and sufficient comparisons.
The labor income share serves as a pivotal measure for assessing how the outcomes of economic development are distributed between labor and capital, with its fluctuations directly shaping the overall income distribution pattern and social equity. This paper employs uncertain regression models to study the relationship between labor income share and four indicators, including trade openness, financial development, government intervention and industrial structure. In addition, examination of the residual plot’s features clarifies the preference for uncertain regression models over probabilistic ones.
Within the framework of uncertainty theory, this paper investigates the optimal control problem for dynamical systems governed by a linear Caputo-type uncertain fractional differential equation. The Cauchy problem of the equation is formulated, and representation formulas for its solutions are derived using the fundamental solution matrix. Based on the informational image of the system’s position together with these formulas, the original uncertain fractional optimal control model is reduced to an auxiliary model driven by an uncertain differential equation, and solved via dynamic programming. It is further shown that the auxiliary model yields the same optimal control and optimal expected value as the original model, which ensures the validity of the proposed approach. As an application, the optimal control problem of wastewater pollutant emissions in China is investigated, and the corresponding optimal allocation of pollution control funds is derived.
This paper proposes a multi-objective capacitated location-routing problem with stochastic demands and time windows applicable in household waste logistics management. The problem involves two interrelated decisions: locating waste transfer stations and routing vehicles through transfer stations and collection points. A solution approach Query based on a squirrel search algorithm with path-relinking, randomized local search, stochastic simulation and non-dominated sorting is introduced to solve the problem. The effects of a vehicle preference index and trapezoidal time windows over total cost and satisfaction are examined through numerical experiments. The approach is tested on benchmark instances and compared with other methods, showing that our algorithm is effective and efficient in finding satisfactory solutions within a reasonable computational time. A real case study is presented to demonstrate the applicability and usefulness of the proposed model and solution method.
This study investigates the optimization of supply chain cooperation using rebate mechanisms under conditions of demand and price uncertainty. By employing uncertainty theory to model the interdependence of these key factors, the main contribution of this research is the development and evaluation of an effective rebate range. This range provides a more adaptable and resilient approach to encouraging collaboration between manufacturers and retailers compared to fixed rebate systems. Through numerical simulations, the study shows that changes in critical parameters, such as the retailer’s expectations of the manufacturer’s supply, production costs, wholesale price, and initial market selling price, have a substantial impact on the optimal order quantity, the boundaries of the rebate range, and the overall performance of the supply chain. The adoption of this rebate range promotes cooperative behavior, facilitates fair distribution of benefits, strengthens resilience in uncertain market conditions, advances the theoretical understanding of rebate mechanisms, and offers practical decision-making support for managers crafting flexible strategies to improve supply chain cooperation efficiency.
Online Portfolio Selection (OLPS) has emerged as a rapidly advancing field at the intersection of financial engineering and artificial intelligence, aimed at maximizing cumulative wealth through sequentially adjusting portfolio allocations in dynamic market environments. The core challenge for online portfolio selection lies in accurately forecasting the prospective yields of volatile assets and deriving best portfolio allocations instantaneously. Traditional approaches often rely on historical return patterns and probabilistic assumptions, which often fail to capture complex temporal dependencies and adequately quantify inherent market uncertainties. To address these limitations, this work studies the OLPS problem under the framework of uncertainty theory and introduces a novel framework that synergistically integrates Long Short-Term Memory (LSTM) networks to generate precise return predictions. Based on this dual-pathway design, the adaptive uncertain mean-absolute deviation optimization model is designed, which dynamically balances uncertainty-adjusted expected return against decomposed risk metrics and transaction costs. Finally, several numerical experiments are conducted and solved to illustrate the efficacy and benefits of the proposed approach.
