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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.

The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

The purpose of this paper is to investigate the pricing strategy and the impact of agents' risk preference in a dual-channel supply chain in which both agents are risk-averse.

The authors make use of the mean-variance (MV) method to measure the risk aversion of the agents and apply Stackelberg game to obtain the optimal strategies of the proposed models. Furthermore, the authors compare the optimal strategies with that in the benchmark model in which no agent is risk-averse.

The authors find that the pricing decisions can be divided into four categories according to the risk attitudes of the agents: the decisions that are independent of two agents' risk attitudes, the decisions that depend on only one agent’s risk attitude (i.e. depend on only manufacturer's risk attitude and depend on only retailer's risk attitude) and the decisions that depend on both agents' risk attitudes. In addition, the authors find that the retail price will be lower and the wholesale price in most cases will be lower than that in the benchmark when at least one agent's risk control is effective; the demand will be always increasing as long as one agent's risk control is effective. Furthermore, compared to the benchmark, a win-win strategy (i.e. Pareto improvement) for the supply chain members can be obtained in a certain range where the agents' risk controls are appropriate.

This research provides a theoretical reference for the managers to make the pricing decisions and the risk control in dual-channel supply chains with heterogeneous preference consumers.

Meteorological disasters pose a significant risk to people’s lives and safety, and accurate prediction of weather-related disaster losses is crucial for bolstering disaster prevention and mitigation capabilities and for addressing the challenges posed by climate change. Based on the uncertainty of meteorological disaster sequences, the damping accumulated autoregressive GM(1,1) model (DAARGM(1,1)) is proposed.

Firstly, the autoregressive terms of system characteristics are added to the damping-accumulated GM(1,1) model, and the partial autocorrelation function (PACF) is used to determine the order of the autoregressive terms. In addition, the optimal damping parameters are determined by the optimization algorithm.

The properties of the model were analyzed in terms of the stability of the model solution and the error of the restored value. By fitting and predicting the losses affected by meteorological disasters and comparing them with the results of four other grey models, the validity of the new model in fitting and prediction was verified.

The dynamic damping trend factor is introduced into the grey generation operator so that the grey model can flexibly adjust the accumulative order of the sequence. On the basis of the damping accumulated grey model, the autoregressive term of the system characteristics is introduced to take into account the influence of the previous data, which is more descriptive of the development trend of the time series itself and increases the effectiveness of the model.

In recent years, online public opinion reversal incidents have been occurring frequently, which has increased the complexity of the evolution of online public opinion, and they have become a difficult issue for public opinion management and control. It is of great significance to explore the regularity of online public opinion reversal.

Combined with the grey characteristics of online public opinion information, a grey graphical evaluation review technique (G-GERT) network model is constructed based on kernel and grey degree, and the frequency, probability and time of online public opinion reversal nodes are calculated using C-marking method and Z-marking method.

Throughout the online public opinion reversal events, there are all repeated outbreak nodes occurring, so the authors regard the repeated occurrence of outbreak nodes as reversal. According to the average frequency, probability and time of repeated outbreak nodes in the G-GERT network model, the authors predict the corresponding key information of reversal. It can simulate the evolution process of public opinion events accurately.

The G-GERT network model based on kernel and grey degree reveals the regulation of public opinion reversal, predicts the frequency, probability and time of reversal nodes, which are the most concerned and difficult issues for decision-makers. The model provides the decision basis and reference for government decision-making departments.

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.

The purpose of this paper is to present a new method about dynamic decision problems with three-parameter grey numbers from other angle of view which not only aggregates the attribute values of alternatives of all the periods, but also excavates changes of attribute values about alternatives between the adjacent periods.

The authors adopt grey target method to calculate the distance between every alternative and the best, worst bull’s eye, the distance between change series and the best, worst change bull’s eye, then both distances can be aggregated to reflect information about two aspects.

This dynamic decision-making method not only aggregates the existing state of alternatives all of the stages, but also excavates the change information from vertical and horizontal direction, the decision result conforming to decision maker’s psychological behavior is obtained though adjusting the priority parameter.

The paper considers on change of alternative’s attribute values from one period to the next period, and the dynamic characteristic has been reflected adequately. The grey target decision-making method reflects the distance between alternative and bull’s eye, the comprehensive target distance between alternative and positive, worst bull’s eye about change series are separately provided. And the final target distance reflecting both existing state and change trend is constructed.

With respect to multi-stage group risk decision-making problems in which all the attribute values take the form of grey number, and the weights of stages and decision makers are unknown, the purpose of this paper is to propose a new decision-making method based on grey target and prospect theory.

First, the sequencing and distance between two grey numbers are introduced. Then, a linear operator with the features of the “rewarding good and punishing bad” is presented based on the grey target given by decision maker, and the prospect value function of each attribute based on the zero reference point is defined. Next, weight models of stages and decision makers are suggested, which are based on restriction of stage fluctuation, the maximum differences of alternatives and the maximum entropy theory. Furthermore, the information of alternatives is aggregated by WA operator, the alternatives are selected by their prospect values.

The comprehensive cumulative prospect values are finally aggregated by WA operator, alternatives are selected or not are judged by the sign of the comprehensive prospect theory, if the prospect value of alternative is negative, the corresponding alternative misses the group decision makers’ grey target, on the contrary, if the prospect value of alternative is positive, the corresponding alternative is dropped into the group decision makers’ grey target, the alternative with positive prospect value whose value is the maximum is selected.

Compared with the traditional decision-making methods using expected utility theory which suppose the decision makers are all completely rational, the proposed method is based on irrational which is more in line with the decision maker’s psychology. And this method considers the decision maker’s psychological expectation values about every attribute, different satisfactory grey target about attributes will directly affect decision-making result.

The purpose of this paper is to explore new ways and lay a solid foundation to solve the problem of reliability growth analysis of major aerospace equipment with various uncertainty data through propose new concepts of general uncertainty data (GUD) and general uncertainty variable (GUV) and build the operation system of GUVs.

The characteristics of reliability growth data of major aerospace equipment and the limitations of current reliability growth models have been analyzed at first. The most commonly used uncertainty system analysis methods of probability statistics, fuzzy mathematics, grey system theory and rough set theory have been introduced. The concepts of GUD and GUV for reliability growth data analysis of major aerospace equipment are proposed. The simplified form of GUV based on the “kernel” and the degree of uncertainty of GUV is defined. Then an operation system of GUVs is built.

(1) The concept of GUD; (2) the concept of GUV; (3) The novel operation rules of GUVs with simplified form.

The method exposed in this paper can be used to integrate complex reliability growth data of major aerospace equipment. The reliability growth models based on GUV can be built for reliability growth evaluation and forecasting of major aerospace equipment in practice. The reliability evaluation example of a solid rocket motor shows that the concept and idea proposed in this paper are feasible. The research of this paper opens up a new way for the analysis of complex uncertainty data of reliability growth of major aerospace equipment. Moreover, the operation of GUVs could be extended to the case of algebraic equation, differential equation and matrix which including GUVs.

The new concepts of GUD and GUV are given for the first time. The novel operation rules of GUVs with simplified form were constructed.

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.