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Intrusion detection maintains the normal activity of the network system by identifying abnormal connections, while intrusion analysis further identifies specific types of abnormality. The current intrusion detection systems (IDSs) have connected intrusion detection, intrusion analysis, and intrusion processing in series so that the system can address network intrusion behaviors of attackers promptly. Most IDSs are constructed with complex models to achieve high-precision intrusion detection and intrusion analysis tasks. The generation of Explainable Artificial Intelligence (XAI) helps to aid in understanding the decision logic of the prediction of IDS for unknown data. It also helps to establish a plausible criterion for further categorized predictions of the type of abnormal data. With this in mind, this paper proposes an XAI-based approach for analyzing network intrusion by the contribution of features of data to prediction results. The Shapley values are used to represent these contributions and are derived from SHapley Additive exPlanations (SHAP). Specific classification criterion is extracted from these contributions for analyzing unknown types of abnormal data. We conducted experiments on seven publicly available intrusion detection datasets. The experimental results have shown that the approach can realize the effective analysis of abnormal data while ensuring high-accuracy detection of network intrusion data. At the same time, when compared to autoencoder and decision tree (DT) which both have prediction and explanation, the proposed approach can get a better overall performance in intrusion detection and intrusion analysis tasks. [ABSTRACT FROM AUTHOR]

The integration of the Industrial Internet of Things (IIoT) and federated learning (FL) can be a promising approach to achieving secure and collaborative AI-driven Industry 4.0 and beyond. FL enables the collaborative training of a global model under the supervision of a central server while ensuring that data remain localized to ensure data privacy. Subsequently, the locally trained models can be aggregated to enhance the global model training process. Nevertheless, the merging of these local models can significantly impact the efficacy of global training due to the diversity of each industry's data. In order to enhance robustness, we propose a Shapley value-based adaptive weighting mechanism that trains the global model as a sequence of cooperative games. The client weights are adjusted based on their Shapley contributions as well as the size and variability of their local datasets in order to improve the model performance. Furthermore, we propose a quantization strategy to mitigate the computational expense of Shapley value computation. Our experiments demonstrate that our method achieves the highest accuracy compared to existing methods due to the efficient assignment of weights. Additionally, our method achieves nearly the same accuracy with significantly lower computational cost by reducing the computation overhead of Shapley value computation in each round of training. [ABSTRACT FROM AUTHOR]

Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. In this paper, we focus on interval game versions of Shapley values. First, we modify Young's strong monotonicity axiom for coalitional games into two versions so that they can be applied to the Shapley mapping and show that this can be axiomatized within the entire class of interval games using either version. Second, we derive the Shapley mapping for specific examples by employing two approaches used in the proof of the axiomatization and argue that our approach effectively works for a wide range of interval games. [ABSTRACT FROM AUTHOR]

Efficient and secure data sharing is paramount for advancing modern digital ecosystems, especially within edge computing environments characterized by resource-constrained nodes and dynamic network topologies. In such settings, privacy preservation, computational efficiency, and system resilience are critical for user engagement and overall system performance. However, existing approaches face three primary challenges: (i) limited optimization of privacy protection and absence of dynamic privacy budget scheduling for resource-constrained scenarios, (ii) static incentive mechanisms that overlook individual differences in data quality and resource consumption, and (iii) inadequate strategies to ensure resilience in environments with limited resources and unstable networks. This paper introduces the Federated Learning-based Dynamic Incentive Allocation Framework (FL-DIAF) to address these issues. FL-DIAF integrates differential privacy into the federated learning paradigm deployed on edge nodes, enabling collaborative model training that safeguards individual data privacy while maintaining computational efficiency and system resilience. Additionally, the framework employs a Shapley value-based dynamic incentive allocation model to ensure equitable and transparent distribution of incentives by accurately quantifying each participant's contribution within an elastic edge computing infrastructure. Comprehensive experimental evaluations on diverse datasets demonstrate that FL-DIAF achieves a 9.573% reduction in the objective function value under typical conditions and attains a 100% task completion rate across all tested resilient edge scenarios. [ABSTRACT FROM AUTHOR]

A global (cooperative) game describes the utility that the whole set of players generates depending on the coalition structure they form. These games were introduced by Gilboa and Lehrer (Int J Game Theory 20:129–147, 1991) who proposed and characterized a generalization of the Shapley value. We introduce two families of point valued solutions that contain the Gilboa–Lehrer value. We characterize each family by means of reasonable properties, which are related to the ones used by Gilboa and Lehrer. [ABSTRACT FROM AUTHOR]

We address the issue of fairly rewarding contributors to a crowdfunded project. We develop a theoretical non-strategic model, and introduce a new reward rule: a contributor's reward depends both on her financial contribution and on the timing of her contribution. Following the axiomatic method used in models of resource sharing, we characterize this new reward rule by a pair of natural axioms. The resulting rewards coincide with the Shapley value of a suitable cooperative game built from the crowdfunding project. This allocation rule conveys a signaling effect: if two contributors make the same financial contribution, the earlier obtains a greater reward. [ABSTRACT FROM AUTHOR]

The effect of water flooding development in low permeability reservoir is generally poor, and CO2 flooding can effectively improve the degree of crude oil recovery. In order to analyze various factors affecting the effect of CO2 -assisted gravity flooding, based on the research mechanism of gas-injection-assisted gravity flooding, a mechanism model of one injection and one production was established to analyze the influence law of geological factors and development factors, and the orthogonal experimental design method and Shapley value method were used for multi-factor analysis. The results show that the positive rhythm reservoir is more suitable for CO2 -assisted gravity flooding. Reservoir dip angle, average permeability and gas injection velocity are positively correlated with development effect. The ratio of vertical permeability to horizontal permeability and the difference of permeability stage were negatively correlated with the development effect. If the ratio of gas injection and dimensionless horizontal well section length is set to 0. 8, the CO2 -assisted gravity flooding effect can be effectively improved. The ratio of vertical permeability to horizontal permeability has the highest influence on CO2 -assisted gravity flooding. The research results provide technical guidance and theoretical support for improving the development effect of CO2 -assisted gravity flooding in low permeability reservoirs. [ABSTRACT FROM AUTHOR]

This paper examines how meteorological factors influence streamflow. It is crucial for water resources planning and management. It develops three Deep Learning (DL) models (Long short-Term Memory (LSTM), Random Forest (RF), and Gradient Boosting Machine (GBM)) and compares their performance with multiple linear regression (MLR). LSTM is identified as the best model, and SHAP is used to analyse the contributions of different factors to streamflow. The model is applied to the Tang River catchment in China. The results indicate that: (1) DL models outperform MLR in non-linear regression; (2) the ranking of meteorological factors contributing to streamflow is: precipitation, evaporation, relative humidity, sunshine duration, ground temperature, and wind speed; (3) these factors affect streamflow within a 12-day lead time, with significant contributions closer to the prediction date; (4) during droughts, precipitation has a reduced effect on streamflow, suggesting that the streamflow is likely recharged by groundwater. The model enhances our understanding of how meteorological factors interact with streamflow dynamics. [ABSTRACT FROM AUTHOR]

The precise identification of maize kernel varieties is essential for germplasm resource management, genetic diversity conservation, and the optimization of agricultural production. To address the need for rapid and non-destructive variety identification, this study developed a novel interpretable machine learning approach that integrates low-field nuclear magnetic resonance (LF-NMR) with morphological image features through an optimized support vector machine (SVM) framework. First, LF-NMR signals were obtained from eleven maize kernel varieties, and ten key features were extracted from the transverse relaxation decay curves. Meanwhile, five image morphological features were selected using the recursive feature elimination (RFE) algorithm. Before modeling, principal component analysis (PCA) was used to determine the distribution features of the internal components for each maize variety. Subsequently, LF-NMR features and image morphological data were integrated to construct a classification model and the SVM hyperparameters were optimized using an improved differential evolution algorithm, achieving a final classification accuracy of 96.36%, which demonstrated strong robustness and precision. The model's interpretability was further enhanced using Shapley values, which revealed the contributions of key features such as Max Signal and Signal at Max Curvature to classification decisions. This study provides an innovative technical solution for the efficient identification of maize varieties, supports the refined management of germplasm resources, and lays a foundation for genetic improvement and agricultural applications. [ABSTRACT FROM AUTHOR]

Collaborative filtering recommendation systems generate personalized recommendation results by analyzing and collaboratively processing a large numerous of user ratings or behavior data. The widespread use of recommendation systems in daily decision-making also brings potential risks of privacy leakage. Recent literature predominantly employs differential privacy to achieve privacy protection, however, many schemes struggle to balance user privacy and recommendation performance effectively. In this work, we present a practical privacy-preserving scheme for user-based collaborative filtering recommendation that utilizes fuzzy C-means clustering and Shapley value, FSPPCFs, aiming to enhance the recommendation performance while ensuring privacy protection. Specifically, (i) we have modified the traditional recommendation scheme by introducing a similarity balance factor integrated into the Pearson similarity algorithm, enhancing recommendation system performance; (ii) FSPPCFs first clusters the dataset through fuzzy C-means clustering and Shapley value, grouping users with similar interests and attributes into the same cluster, thereby providing more accurate data support for recommendations. Then, differential privacy is used to achieve the user’s personal privacy protection when selecting the neighbor set from the target cluster. Finally, it is theoretically proved that our scheme satisfies differential privacy. Experimental results illustrate that our scheme significantly outperforms existing methods. [ABSTRACT FROM AUTHOR]

With the rapid development of e-commerce, the traditional trade mode of forest products has undergone significant changes. Logistics as a key factor to support e-commerce trade is particularly important to build a reasonable e-commerce logistics model of forest products. In the logistics service industry, the issue of cooperative profit allocation of logistics alliance has been crucial and prevalent. However, logistics alliances often face the problem of incomplete information, such as the ambiguity of transportation cost and driving distance, which makes it difficult to effectively apply many classical cooperative game solutions. Therefore, this paper introduces an improved Shapley value for cooperative games in fuzzy situations regarding unclear profit allocation in e-commerce logistics alliance of forest products. This value maximizes the satisfaction of the players by minimizing the contribution excess, according to which the trapezoidal fuzzy number least square contribution is calculated. Based on this, we replace the marginal contribution of the classical Shapley value with this least square contribution, thus creating the improved Shapley value with trapezoidal fuzzy numbers. Through the verification of actual cases, this method not only has theoretical value, but also provides effective guidance for the actual profit allocation of e-commerce logistics alliance of forest products, which helps to promote the stability and sustainable development of alliance. [ABSTRACT FROM AUTHOR]

Blockchain-based E-participation systems significantly enhance transparency, data integrity, and security compared to traditional E-participation methods. However, existing systems often face challenges, such as inefficient attribute sampling in Zero-Knowledge Proof (ZKP)-based systems and the absence of effective differential reward mechanisms to distinguish between sincere and insincere participants. This paper introduces a blockchain-based E-participation framework designed to address these challenges. The proposed approach improves attribute sampling in ZKP-based systems by incorporating attribute keys, enabling efficient and secure sampling of participants without compromising privacy. This ensures that only eligible participants are selected while maintaining the integrity of the sampling process. Furthermore, the framework uses Shapley Values to implement a robust differential reward system that fairly compensates participants based on their sincerity, encouraging genuine contributions while penalizing insincere behavior. The security of the proposed framework is rigorously validated through a comprehensive security analysis, and its performance is thoroughly evaluated to demonstrate its effectiveness. Additionally, the feasibility of this approach is demonstrated through a prototype with real-world participants, highlighting its practicality and potential for deployment in E-participation systems.

Energy communities (ECs) are an increasingly studied path toward improving prosumer coordination. A central challenge of ECs is to allocate cost savings fairly to members. While many allocation mechanisms have been developed, existing literature does not account for the implications of inaccurate forecasts on the fairness of the allocation. We introduce a set of fairness conditions for imperfect knowledge allocation and show that these conditions constitute a Pareto front. We demonstrate how a well-established allocation scheme, the Shapley value mechanism (SVM), has unfavorable consequences for flexibility-providing community members and generally does not yield solutions on this Pareto front. In contrast, we interpret dispatch cost under imperfect knowledge as being composed of two components. The first represents the cost under perfect knowledge, and the second represents the cost arising from inaccurate forecasts. Our proposed mechanism extends an SVM-based allocation of the perfect knowledge cost by allocating the remaining cost in a way that guarantees finding solutions on the Pareto front. To this end, we formulate a convex multi-objective optimization problem that can efficiently be solved as a linear or quadratic program.

Tree models have made an impressive progress during the past years, while an important problem is to understand how these models predict, in particular for critical applications such as finance and medicine. For this issue, most previous works measured the importance of individual features. In this work, we consider the interpretation of feature groups, which is more effective to capture intrinsic structures and correlations of multiple features. We propose the Baseline Group Shapley value (short for BGShapvalue) to calculate the importance of a feature group for tree models. We further develop a polynomial algorithm, BGShapTree, to deal with the sum of exponential terms in the BGShapvalue. The basic idea is to decompose the BGShapvalue into leaves' weights and exploit the relationships between features and leaves. Based on this idea, we could greedily search salient feature groups with large BGShapvalues. Extensive experiments have validated the effectiveness of our approach, in comparison with state-of-the-art methods on the interpretation of tree models. [ABSTRACT FROM AUTHOR]

Abstract Collaborative filtering recommendation systems generate personalized recommendation results by analyzing and collaboratively processing a large numerous of user ratings or behavior data. The widespread use of recommendation systems in daily decision-making also brings potential risks of privacy leakage. Recent literature predominantly employs differential privacy to achieve privacy protection, however, many schemes struggle to balance user privacy and recommendation performance effectively. In this work, we present a practical privacy-preserving scheme for user-based collaborative filtering recommendation that utilizes fuzzy C-means clustering and Shapley value, FSPPCFs, aiming to enhance the recommendation performance while ensuring privacy protection. Specifically, (i) we have modified the traditional recommendation scheme by introducing a similarity balance factor integrated into the Pearson similarity algorithm, enhancing recommendation system performance; (ii) FSPPCFs first clusters the dataset through fuzzy C-means clustering and Shapley value, grouping users with similar interests and attributes into the same cluster, thereby providing more accurate data support for recommendations. Then, differential privacy is used to achieve the user’s personal privacy protection when selecting the neighbor set from the target cluster. Finally, it is theoretically proved that our scheme satisfies differential privacy. Experimental results illustrate that our scheme significantly outperforms existing methods.

Introduction: In cloud computing, a common idea to reduce operation costs and improve service quality is to study task scheduling algorithms. Methods: To better allocate virtual machine resources, a virtual machine resource scheduling algorithm, Shapley value method–genetic algorithm (SVM-GA) is proposed. This algorithm uses the SVM to obtain the contribution values of each component of the virtual machine, refine the topological network, and achieve the optimal solution of scheduling by the genetic algorithm. Results and Discussion: CloudSim simulation results indicate that SVM-GA has the lowest total task completion time when compared with existing intelligent optimization algorithms (such as the max–min algorithm, logistic regression algorithm, and differential evolution algorithm) with the same number of tasks, and the total task time is 25, 55, 81, 112, 145, and 175 s for 200, 400, 600, 800, 1,000, and 1,200 tasks, respectively. As the number of evolutionary generations increases, the ability of SVM-GA to reach the optimal solution of the model increases. In the simulated light load case, the SVM-GA migration time and Q10 migration count optimal solutions are slightly inferior to those of the logistic regression algorithm (3.02 s > 2.38 s; 1,129 times >999 times), but the migration energy consumption and service level agreement violation rate optimal solutions are superior. The SVM-GAA's performance in the heavy load case is similar to that in the light load case. The experiments show the feasibility of the algorithm proposed in the study. [ABSTRACT FROM AUTHOR]

The profit and loss (P &L) attribution for each business year into different risk factors (e.g., interest rates, credit spreads, foreign exchange rate etc.) is a regulatory requirement, e.g., under Solvency 2. Three different decomposition principles are prevalent: one-at-a-time (OAT), sequential updating (SU) and average sequential updating (ASU) decompositions. In this research, using financial market data from 2003 to 2022, we demonstrate that the OAT decomposition can generate significant unexplained P &L and that the SU decompositions depends significantly on the order or labeling of the risk factors. On the basis of an investment in a foreign stock, we further explain that the SU decomposition is not able to identify all relevant risk factors. This potentially effects the hedging strategy of the portfolio manager. In conclusion, we suggest to use the ASU decomposition in practice. [ABSTRACT FROM AUTHOR]

The splitting tensile strength of concrete is crucial for structural integrity, as tensile stresses from load and environmental changes often lead to cracking. This study investigates the effectiveness of advanced ensemble machine-learning models, including LightGBM, GBRT, XGBoost, and AdaBoost, in accurately predicting the splitting tensile strength of silica fume-enhanced concrete. Using a robust database split into training (80%) and testing (20%) sets, we assessed model performance through R2, RMSE, and MAE metrics. Results demonstrate that GBRT and XGBoost achieved superior predictive accuracy, with R2 scores reaching 0.999 in training and high precision in testing (XGBoost: R2 = 0.965, RMSE = 0.337; GBRT: R2 = 0.955, RMSE = 0.381), surpassing both LightGBM and AdaBoost. This study highlights GBRT and XGBoost as reliable, efficient alternatives to traditional testing methods, offering substantial time and cost savings. Additionally, SHapley Additive exPlanations (SHAP) analysis was conducted to identify key input features and to elucidate their influence on splitting tensile strength, providing valuable insights into the predictive behavior of silica fume-enhanced concrete. The SHAP analysis reveals that the water-to-binder ratio and curing duration are the most critical factors influencing the splitting tensile strength of silica fume concrete. [ABSTRACT FROM AUTHOR]

Summary: Relay selection plays a crucial role in enhancing the performance of wireless networks particularly in the context of cognitive radio (CR) systems with energy harvesters. In this paper, we propose a novel approach, namely, CGAPSO Shapley, for the best relay selection while simultaneously optimizing the parameters of signal‐to‐interference‐plus‐noise ratio (SINR), throughput, and outage probability. The CGAPSO Shapley algorithm combines the Shapley value, a cooperative game theory concept, with cellular genetic algorithm particle swarm optimization (CGAPSO) to achieve effective and efficient optimization of relay selection. The CGAPSO framework provides a hybrid structure that integrates cellular genetic algorithm (CGA) and particle swarm optimization (PSO), enabling simultaneous evolution of the population and particles within cells. The incorporation of the Shapley value and the hybrid CGAPSO framework enables effective exploration of the solution space and provides decision‐makers with comprehensive insights for relay selection. By utilizing the Shapley value, we assign weights to the relay nodes based on their contributions to the overall optimization objectives, considering their CR capabilities and energy harvesting capabilities. Some benchmark test functions are used to compare the hybrid algorithm with both the standard CGAPSO, Particle swarm optimization gravitational search algorithm (PSOGSA) and PSO algorithms in evolving best solution. The results show the hybrid algorithm possesses a better capability to escape from local optimums with faster convergence than the standard algorithms. The novel CGAPSO Shapley approach achieves an outage probability of 0.323324, marking a significant improvement of 60% over the outage probability achieved with conventional approach. [ABSTRACT FROM AUTHOR]

Socially responsible investments represent the heart of a sustainable and inclusive economy. The goals set by the regulatory framework have encouraged the integration of responsible concerns into the corporate business strategy. In this paper, we present an operation research design under a risk management perspective that adjusts the portfolio selection problem for the ethical values of investors. We focus on the firms of the Euro Stoxx 50 during the years 2007–2019 and cluster the companies according to the Environmental Score (E). For each cluster, we build a portfolio that minimizes the Conditional Value-at-Risk (CVaR) introducing the constraint on the E into the optimization problem. We compute the Shapley Value for each portfolio using the minimized CVaR and the optimized E as the characteristic functions to yield, respectively, the contribution of the portfolios to the public welfare in terms of the exposure to the tail market risk and the required environmental commitment to mitigate it. The cluster analysis shows that the efforts of the firms to embrace environmental concerns are paid off with generally lower contribution to the tail market risk. From the two characterizations of the Shapley Value, the computation of well-known measures of financial performance (Sharpe, Sortino, and Calmar ratios) reveals that optimal portfolio choices should prioritize the environmental commitment of the companies. [ABSTRACT FROM AUTHOR]

We unified the recent literature with the goal to contribute to the discussion on how genetic diversity might best be conserved. We argue that this decision will be guided by how genomic variation is distributed among manageable populations (i.e., its spatial structure), the degree to which adaptive potential is best predicted by variation across the entire genome or the subset of that variation that is identified as putatively adaptive (i.e., its genomic structure), and whether we are managing species as single entities or as collections of diversifying lineages. The distribution of genetic variation and our ultimate goal will have practical implications for on-the-ground management. If adaptive variation is largely polygenic or responsive to change, its spatial structure might be broadly governed by the forces determining genome-wide variation (linked selection, drift, and gene flow), making measurement and prioritization straightforward. If we are managing species as single entities, then population-level prioritization schemes are possible so as to maximize future pooled genetic variation. We outline one such scheme based on the popular Shapley value from cooperative game theory that considers the relative genetic contribution of a population to an unknown future collection of populations. [ABSTRACT FROM AUTHOR]