The weighted surplus division value is defined in this paper, which allocates to each player his individual worth and then divides the surplus payoff with respect to the weight coefficients. This value can be characterized from three different angles. First, it can be obtained analogously to the scenario of getting the procedural value whereby the surplus is distributed among all players instead of among the predecessors. Second, endowing the exogenous weight to the surplus brings about the asymmetry of the distribution. We define the disweighted variance of complaints to remove the effect of the weight and prove the weighted surplus division value is the unique solution of an optimization model. Lastly, the paper offers axiomatic characterizations of the weighted surplus division value through proposing new properties, including the ω -symmetry for zero-normalized game and individual equity.

The paper defines a new value called the weighted nonseparable cost value (weighted-NSC value), which divides the nonseparable cost on the ground of an exogenous attached weight and compromises egalitarianism and utilitarianism of a value flexibly. First, we construct an optimization model to minimize the deweighted variance of complaint and define its optimal solution to be the weighted-NSC value. Second, a process is set up to acquire the weighted-NSC value, which enlarges the traditional procedural values. In the process, one player’s marginal contribution is divided up by all participants rather than merely restricted within his precursors. Lastly, adopting the weight in defining a value destructs the classical symmetry. This promotes the definition of ω-symmetry for the grand-marginal normalized game to defend against the effect of weight and axiomatically sculptures the weighted-NSC value. Dual dummifying player property is also applied to characterize the new defined value.

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Under the background of intelligent times based on information technology, the analysis and replacement of outliers become particularly critical for databases in the face of massive sequential data streams. In order to improve the effectiveness and practicability of the detection method, this paper determines the abnormal scores of data points in a specific data set by using the K-Sigma algorithm of the Monte Carlo method, adaptively adjusts the k value according to the abnormal scores, and marks the abnormal points. The advantages of the traditional k-sigma algorithm are fast operation speed and theoretical basis, while the disadvantages are that each index dimension is determined independently. However, in industrial production, due to the multi-index dimension of time series data, multiple size indicators of a data set are related to each other. Therefore, it is necessary to comprehensively consider whether an anomaly is abnormal by combining it with the data of other indicators. In addition, when there are no outliers in the data set, the traditional k-sigma algorithm is used to take the mean and variance of the data set as parameters. Due to the limitations of the data set itself, some data points will be mislabeled as outliers. Through the k-sigma algorithm based on the Monte Carlo method, we can effectively solve the above problems. The k-sigma algorithm based on the Monte Carlo method can generate a normal distribution according to the distribution of original data points, and extract a large quantity of data from the distribution to generate Monte Carlo data set. The Mahalanobis distance li from each sample point to the mean in the Monte Carlo data set is calculated and compared with the Mahalanobis distance lj from the samples to be detected to the mean in the original data set. According to the number of sample points satisfying li < lj in the Monte Carlo data set, the value of the parameter kj is determined adaptively, and thus the outliers are determined. We implemented the k-sigma algorithm based on the Monte Carlo method through python, evaluated the effectiveness of the algorithm by accuracy, recall rate, and F1 score, and compared it with some machine learning algorithms. The results verified the feasibility and effectiveness of the algorithm, which can be used for real-time anomaly detection in the energy management database.