This paper proposes an Innovative Adaptive Particle Swarm Grey Wolf Algorithm based on Self-constructing Fuzzy (SFAPSO-GWO) to solve the optimization problem of complex functions under practical engineering conditions. The algorithm dynamically optimizes the core parameters of the fuzzy system according to the characteristics of different optimization stages, balancing the flexibility and stability of fuzzy reasoning. Meanwhile, an innovative population update collaborative guidance mechanism is designed, which breaks the single collaborative logic of static weighting or stage switching in traditional PSO-GWO hybrid algorithms and enables in-depth integration of the two algorithms’ core guidance information. Experiments on Rosenbrock’s function show that compared with PSO-GWO, HGWO-PSO, and APSO-GWO, SFAPSO-GWO reduces convergence time by 78.90
Application domains such as stock price prediction, sales forecasting, weather prediction, etc., are well studied regression problems. These applications are meaningful only when they can be scalable. However, not many machine learning algorithms, including support vector regression, have been designed to address the problem of scalability, restricting its usage to real-life applications. All variants of Support Vector Regression (SVR) solve quadratic programming problems, which leads to high computational cost and hence restricts its usability, especially when dealing with large size datasets. In addition, SVR ϵ -insensitive loss function is sensitive to noise and outliers and therefore can adversely affect regression performance. To address these problems, we propose Fuzzy Granular Ball Support Vector Regression (FGBSVR) to tackle the regression problem using the concept of fuzzy granular regression balls. The proposed Fuzzy Granular Regression Balls (FGRBs) are useful in simplifying complex and ambiguous data spaces for machine learning tasks; however, to the best of our knowledge, they have not been investigated for the fuzzy regression problem. Granular regression balls group the data points into balls based on their proximity, which considers the discretization method for continuous valued attributes. Further, the Pythagorean fuzzy score is determined with each granular regression ball, which addresses the issue of the importance of data points for identifying the regressor and facilitates the construction of fuzzy granular regression balls and hence its extension to fuzzy granular support vector regression. The proposed method is evaluated on several benchmark datasets and it outperforms existing state-of-the-art approaches.
In group decision-making research, the maximum utility consensus with limited budgets has received considerable attention. However, existing studies overlook the behavior of non-cooperative games among decision-makers under limited consensus budgets, which may result in unstable consensus outcomes. To address this issue, we introduce a novel maximum utility consensus model based on the non-cooperative game framework (NMUCM), in which each decision-maker seeks to maximize individual utility while satisfying the required consensus level and budget constraints. In NMUCM, the individual utility integrates the compensation utility, the recognition utility, and the confidence utility, which not only comprehensively captures the utility preferences of individual decision-makers but also effectively characterizes the heterogeneity of preferences among group members. Interestingly, the consensus generated by NMUCM is a generalized Nash equilibrium. This implies that no decision-maker can unilaterally alter their adjusted opinion to improve individual utility, which illustrates the stability of the obtained consensus. For different decision-making scenarios, we prove the existence of generalized Nash equilibria for NMUCM. Furthermore, a regularized Gauss-Seidel algorithm is developed to compute a generalized Nash equilibrium of NMUCM. To prevent the unreasonable adjustments of decision-makers, we introduce a new feedback regulation mechanism based on unit compensation costs. Building upon these, we propose a new consensus mechanism. Finally, an application to green supply chain management demonstrates the effectiveness of the proposed consensus mechanism.
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.
