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The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

With the prosperity of grey extension models, the form and structure of grey forecasting models tend to be complicated. How to select the appropriate model structure according to the data characteristics has become an important topic. The purpose of this paper is to design a structure selection method for the grey multivariate model.

The linear correction term is introduced into the grey model, then the nonhomogeneous grey multivariable model with convolution integral [NGMC(1,N)] is proposed. Then, by incorporating the least absolute shrinkage and selection operator (LASSO), the model parameters are compressed and estimated based on the least angle regression (LARS) algorithm.

By adjusting the values of the parameters, the NGMC(1,N) model can derive various structures of grey models, which shows the structural adaptability of the NGMC(1,N) model. Based on the geometric interpretation of the LASSO method, the structure selection of the grey model can be transformed into sparse parameter estimation, and the structure selection can be realized by LASSO estimation.

This paper not only provides an effective method to identify the key factors of the agricultural drought vulnerability, but also presents a practical model to predict the agricultural drought vulnerability.

Based on the LASSO method, a structure selection algorithm for the NGMC(1,N) model is designed, and the structure selection method is applied to the vulnerability prediction of agricultural drought in Puyang City, Henan Province.

The purpose of this paper is to examine the effectiveness of the multivariable grey prediction model in deformation forecasting.

Deformation in a dam can be seen because of many factors but without any doubt, the most influential factor is the water level. In this study, the deformation level of a point in the Keban Dam crest has been tried to be forecasted depending on the water level by the multivariable grey model GM(1,N). Regression analysis was used to test the accuracy of the prediction results obtained using the grey prediction model.

The results show that there is a great consistency between the grey prediction values and the actual values, and that the GM(1,N) produces more reliable results than the regression analysis. Based on the results, it can be concluded that the GM(1,N) is a very reliable estimation model for limited data conditions.

Different from the other studies in the literature, this study investigates deformation in a dam subject to the water level in the dam reservoir. The main contribution of the study to the literature is to suggest a relatively new procedure for estimating the deformation in the dams based on the water level.

Aiming at the traditional multivariate grey forecasting model only considers the modelling of real numbers; therefore, the purpose of this paper is to construct an MGM(1, m) model based on the interval grey number sequences according to the grey modelling theory.

First, the multivariable grey number sequences are transformed into the kernel and grey radius sequences which are two feature sequences of interval grey number sequences. Then the MGM(1, m) model for kernel sequences and grey radius sequences are established, respectively. Finally, the simulation and prediction of the upper and lower bounds of the interval grey number sequences are realized by the reductive calculation of the predicted values of the kernel and grey radius.

The model is applied to the prediction of visibility and relative humidity, the identification factors of the haze. The results show that the model has high accuracy on the simulation and prediction of multivariable grey number sequences, which is reasonable and practical.

The main contribution of this paper is to propose a method to simulate and forecast the multivariable grey number sequence that is to establish the prediction models for the whitening sequences of multivariable grey number sequences which are kernel and grey radius sequences and extend the possibility boundary of kernel by grey radius. The model can reflect the development trend of multivariable grey number sequence accurately. When the grey information is continuously complemented, the multivariable grey number prediction model is transformed into the traditional MGM(1, m) model. Therefore, the MGM(1, m) model based on interval grey number sequence is the generalisation and expansion of the traditional MGM(1, m) model.

This study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.

In this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.

The results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.

The paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.

High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model.

Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships.

The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021.

The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models.

The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning.

A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

The purpose of this study is to make a prediction of the R&D output of China from the perspective of R&D institutions and put forward a set of policy recommendations for further development of the science and technology in China.

In this paper, an improved discrete grey multivariable model is proposed, which takes both the interaction effects and the accumulative effects into account. As the current research on China's R&D activities is generally based on the perspective of universities or industrial enterprises above designated size while few studies put their focus on R&D institutions, this paper applies the proposed model to carry out an empirical analysis based on the data of China's R&D institutions from 2009 to 2019. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of the R&D output in China's R&D institutions is conducted into a future horizon from 2020 to 2023 by using the model.

The results indicate that China's R&D institutions have a good development trend and broad prospects, which is closely related to China's long-term investment in science and technology. Additionally, the R&D inputs of China possess obvious interaction effects and accumulative effects.

The paper considers the interaction effects and the accumulative effects of R&D inputs simultaneously and proposes an improved discrete grey multivariable model, which fills the gap in previous studies.

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

With the development of economy, China’s OFDI constantly increase in recent year. Meanwhile, OFDI has spillover effect on economic development and technological development of home country. Thus, accurate OFDI prediction is a prerequisite for the effective development of international investment strategies. The purpose of this paper is to predict China’s OFDI accurately using a novel multivariable grey prediction model with Fourier series.

This paper applied a multivariable grey prediction model, GM(1,N), to forecast China’s OFDI. In order to improve the prediction accuracy and without changing local characteristics of grey model prediction, this paper proposed a novel grey prediction model to improve the performance of the traditional GM(1,N) model by combining with residual modification model using GM(1,1) model and Fourier series.

The coefficients indicate that the export and GDP have positive influence on China’s OFDI, and, according to the prediction result, China’s OFDI shows a growing trend in next five years.

This paper proposed an effective multivariable grey prediction model that combined the traditional GM(1,N) model with a residual modification model in order to predict China’s OFDI. Accurate forecasting of OFDI provides reference for the Chinese Government to implement international investment strategies.