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In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

The purpose of this paper is to explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

The purpose of this paper is to establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.

The purpose of this paper is to put forward the grey relational decision-making model of three-parameter interval grey number based on Analytic Hierarchy Process (AHP) and Data Envelopment Analysis (DEA), based on the previous study of grey relational decision-making model, and it considers the advantages of the decision-making schemes and the subjective preferences of decision makers.

First of all, through AHP, the preference of each index is analyzed and the index weight is determined. Second, the DEA model is adopted to obtain the index weight from the perspective of the most beneficial to each scheme and objectively reflect the advantages of different schemes. Then, assign the comprehensive weights to each index of the grey relational decision-making model of three-parameter interval grey number, and calculate the grey relation degree of each scheme to rank the schemes.

The effectiveness of the model is proved by an example of carrier aircraft selection.

The applicability of this model is analyzed by taking carrier aircraft selection as an example. In fact, this model can also be widely used in agriculture, industry, economy, society and other fields.

In this paper, the combination of AHP and DEA is used to determine the index weight. Based on which, the grey relation degree under the three-parameter interval grey number is calculated. It intended the application space of the grey relational decision-making model.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

In order to explore a new estimation approach of hyperspectral estimation, this paper aims to establish a hyperspectral estimation model of soil organic matter content with the principal gradient grey information based on the grey information theory.

Firstly, the estimation factors are selected by transforming the spectral data. The eigenvalue matrix of the modelling samples is converted into grey information matrix by using the method of increasing information and taking large, and the principal gradient grey information of modelling samples is calculated by using the method of pro-information interpolation and straight-line interpolation, respectively, and the hyperspectral estimation model of soil organic matter content is established. Then, the positive and inverse grey relational degree are used to identify the principal gradient information quantity of the test samples corresponding to the known patterns, and the cubic polynomial method is used to optimize the principal gradient information quantity for improving estimation accuracy. Finally, the established model is used to estimate the soil organic matter content of Zhangqiu and Jiyang District of Jinan City, Shandong Province.

The results show that the model has the higher estimation accuracy, among the average relative error of 23 test samples is 5.7524%, and the determination coefficient is 0.9002. Compared with the commonly used methods such as multiple linear regression, support vector machine and BP neural network, the hyperspectral estimation accuracy of soil organic matter content is significantly improved. The application example shows that the estimation model proposed in this paper is feasible and effective.

The estimation model in this paper not only fully excavates and utilizes the internal grey information of known samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a new hyperspectral estimation model of soil organic matter content based on the principal gradient grey information and effectively dealing with the randomness and grey uncertainty in spectral estimation.

This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.

Based on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.

The results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R² = 0.924, and the average relative error is 6.608%.

Studies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.

The paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

The purpose of this paper is to solve the comprehensive evaluation of the equipment maintainability level based on grey system theory, and make an analysis of the corresponding influencing factors and their prioritization process.

Considering the diversity, uncertainty and small sample size of the influencing factors of the equipment maintainability level, a multilayer evaluation attribute system is set up, and the grey relational method is utilized to assess the equipment's comprehensive maintainability. First, the bottom layer relational coefficient and weighted relational degree are analyzed, and, by means of the focus of relational degree through the bottom layer to top layer, the general evaluation of the equipment maintainability is carried out. Second, the equipment maintainability level and its influencing factors model, i.e. GM(1,N) model are set up, and the prioritization of the influencing factors is achieved through the comparison of the size of the model drive coefficients. Finally, the practical example calculation results show that this method has not only realized a sensible and effective evaluation of the equipment maintainability level, but also provided a prioritization of the influencing factors, which helps to focus attention on the major influencing factors and make this method of significant engineering application value in the improvement of the equipment maintainability level.

The modeling of electronic equipment maintainability level and analysis of its corresponding practical example prove that grey system theory could not only perform a comprehensive evaluation of the equipment maintainability level, but also provide a quantitative analysis of its various influencing factors, whereas, other methods such as fuzzy mathematics, etc. can only make a general evaluation of the equipment maintainability level.

This paper has realized an integral evaluation of the equipment maintainability level and has made an analysis of the prioritization of its various influencing factors. These investigation results could be introduced as a promising innovative idea in the evaluation of the equipments' other performances and the prioritization of its various corresponding influencing factors.

Considering the diversity and uncertainty of influencing factors of the equipment maintainability level, this paper has realized a multilayer evaluation attribute system to perform a comprehensive evaluation of equipment maintainability level by means of weighted grey relational degree model. Furthermore, the prioritization of its various influencing factors is achieved based on the GM(1,N) model.

Seasonal fluctuation interference often affects the relational analysis of economic time series. The main purpose of this paper is to propose a new grey relational model for relational analysis of seasonal time series and apply it to identify and eliminate the influence of seasonal fluctuation of retail sales of consumer goods in China.

First, the whole quarterly time series is divided into four groups by data grouping method. Each group only contains the time series data in the same quarter. Then, the new series of four-quarters are used to establish the grey correlation model and calculate its correlation coefficient. Finally, the correlation degree of factors in each group of data was calculated and sorted to determine its importance.

The data grouping method can effectively reflect the correlation between time series in different quarters and eliminate the influence of seasonal fluctuation.

In this paper, the main factors influencing the quarterly fluctuations of retail sales of consumer goods in China are explored by using the grouped grey correlation model. The results show that the main factors are different from quarter to quarter: in the first quarter, the main factors are money supply, tax and per capita disposable income of rural residents. In the second quarter are money supply, fiscal expenditure and tax. In the third quarter are money supply, fiscal expenditure and per capita disposable income of rural residents. In the fourth quarter are money supply, fiscal expenditure and tax.

This paper successfully realizes the application of grey relational model in quarterly time series and extends the applicable scope of grey relational model.

The purpose of this study is to construct a gray relational model based on information diffusion to avoid rank reversal when the available decision information is insufficient, or the decision objects vary.

Considering that the sample dependence of the ideal sequence selection in gray relational decision-making is based on case sampling, which causes the phenomenon of rank reversal, this study designs an ideal point diffusion method based on the development trend and distribution skewness of the sample information. In this method, a gray relational model for sample classification is constructed using a virtual-ideal sequence. Subsequently, an optimization model is established to obtain the criteria weights and classification radius values that minimize the deviation between the comprehensive relational degree of the classification object and the critical value.

The rank-reversal problem in gray relational models could drive decision-makers away from using this method. The results of this study demonstrate that the proposed gray relational model based on information diffusion and virtual-ideal sequencing can effectively avoid rank reversal. The method is applied to classify 31 brownfield redevelopment projects based on available interval gray information. The case analysis verifies the rationality and feasibility of the model.

This study proposes a robust method for ideal point choice when the decision information is limited or dynamic. This method can reduce the influence of ideal sequence changes in gray relational models on decision-making results considerably better than other approaches.