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The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

As an important measure to promote sustainable development, green finance has developed rapidly in recent years. In order to comprehensively analyze the positive and negative indicators of the influencing factors of green finance, this paper puts forward a grey relational method of spatial-temporal panel data from the perspective of the development trend of the object dimension indicators and the performance difference between the time dimension indicators.

From the different perspectives of object dimension and time dimension, the positive and negative indicators are standardized differently considering the reverse of indicators and characterizing factors. The grey absolute relational degree is used to define the matrix sequence. This method reflects the development trend of objects in time and the difference characteristics among objects, which comprehensively represents the correlation between the reference panel and the comparison panel.

The results show that: (1) The object dimension reflects the internal driving force of the development of green finance in each provincial administrative region and the time dimension reflects the relationship between regional differences of influencing factors and green finance. (2) From the object dimension, the influencing factors of green finance from high to low are economic development potential, economic development level, air temperature, policy support, green innovation and air quality. (3) From the time dimension, the influencing factors of green finance from high to low are green innovation, air quality, economic development potential, economic development level, policy support and air temperature.

The different standardized processing methods of positive and negative indicators proposed in this paper not only eliminate the sample dimension, but also study the grey relational degree among the indicator panels from different reference dimensions. The proposed model is applied to identify the influencing factors of green finance, which expands the practical application scope of the grey relational model. The research results can provide reference for relevant departments to better promote the development of green finance.

Green economy and economic development with high quality have set higher requirements for the development of the urban logistics industry. It can grasp the recent development level of the urban logistics industry by measuring its environmental efficiency to guide its future development direction. The purpose of this study is to improve the environmental efficiency and development level of the urban logistics industry by using a reasonable evaluation method.

This paper uses information entropy to directly aggregate index weights from different models to acquire comprehensive index weights (CIWs) for calculating peer-evaluation efficiency. Then, we weight self and peer-efficiencies to obtain final efficiency. The environmental efficiencies of the urban logistics industry in Anhui Province in 2019 are obtained according to the above method.

Several findings are summarized below. The logistics industry in Anhui is in urgent need of improving environmental efficiency. The environmental efficiency of the logistics industry in North Anhui is the highest one, showing that the logistics industry in North Anhui has achieved a relative balance between economic development and environmental protection. Their final cross-efficiency values based on the CIWs are smaller than those based on the comprehensive efficiency. And the environmental efficiency of almost all urban logistics industries is lower than its economic efficiency. The findings show that the proposed method is feasible and more reasonable. More economic implications and suggestions are proposed.

This paper proposes an extended cross-efficiency evaluation method based on information entropy to measure the environmental efficiency of the urban logistics industry, effectively avoiding the overestimation of efficiency results.

In the process of group decision-making, there may be multilayer subjects. In other words, members of the decision-making group may come from different layers and there is interest game among decision experts. Therefore, it is an extremely important topic to aggregate the information of decision experts who are involved in hierarchical relations and gaming relations so as to effectively address game conflicts and reach game cooperation.

First, a programming model is established to minimize the difference of expert opinions in hierarchical decision-making, and the method to solve the optimal solution is given. Second, the cooperative game model and its properties are discussed by using cooperative game and Shapley value, and the method to determine the weight vector between layers is also proposed.

This model can quickly aggregate information and achieve game equilibrium among decision-makers with hierarchical relationships. It can be widely used in decision evaluation with hierarchy structure and has certain practical value.

In order to solve the problem that experts at different levels may have conflicts of interest in multilayer grey situation group decision-making process, cooperative game and Shapley value theory are introduced into the study, and a multilayer grey situation group decision-making model based on cooperative game is constructed. The validity and practicability of the model are illustrated by an example.

With respect to the multiple-attribute decision-making problem with subjective preference for a certain attribute whose weight-value range have been given over other attributes whose weight values are unknown, a method based on the mean value of the grey number is proposed to analyse the decision-making problem. This method is used to choose a supply-chain partner under the condition that the decision makers have a preference for a certain attribute of various alternatives. The paper aims to discuss these issues.

First, the middle value of the preferred attribute’s weight-value range is supposed to be its weight value according to the content of the mean value of the grey number. Second, to reflect the decision maker’s subjective preference information, an improved optimisation model that requests the minimum deviation between the actual and expected numerical value of each attribute is constructed to assess the attributes’ weights. Third, the correlated degree and the correlation matrix, which are determined by the weight values of all attributes, are used to rank all the alternatives.

This paper provides a method for making a decision when decision makers have a preference for a certain attribute from an array of various alternatives, and the range of the certain attribute’s weight value is given but the weight value of the other attributes is unknown. When applied to supply-chain partner selection, this method proves feasible and effective.

This method is feasible and effective when applied to supply-chain partner selection, and can be applied to other kinds of decision-making problems. This means it has significant theoretical importance and extensive practical value.

Based on the mean value of the grey number, an optimisation model is built to determine the importance degree of each attribute, then the correlated degree of each alternative is combined to rank all the alternatives. This method can suit the decision makers’ subjective preference for a certain attribute well.

Independent directors are important corporate decision participants and makers. Based on the Chinese cultural background, this paper interprets the listing order of independent directors as independent directors’ status, exploring their influence on the corporate research and development (R&D) behavior.

This paper studies A-share listed firms in China from 2008 to 2018 as the sample. The main method is ordinary least square (OLS) regression. We also use other methods to deal with endogenous problems, such as the firm fixed effect method, change model method, two-stage instrumental variable method, and Heckman two-stage method.

(1) Higher independent directors’ status attribute to more effective exertion of supervision and consultation function, and positively enhance the corporate R&D investment. The increase of the independent director’ status by one standard deviation will increase the R&D investment by 4.6%. (2) The above effect is more influential in firms with stronger traditional culture atmosphere, higher information opacity and higher performance volatility. (3) High-status independent directors promote R&D investment by improving the scientificity of R&D evaluation and reducing information asymmetry. (4) The enhancing effect of independent director’ status on R&D investment is positively associated with the firm’s patent output and market value.

This paper contributes to understanding the relationship between the independent directors’ status and their duty execution from an embedded cultural background perspective. The findings of the study enlighten the improvement of corporate governance efficiency and the healthy development of the capital market.