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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.

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.

The purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences.

The definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied.

The negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility.

The proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model.

The definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

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.

The purpose of this paper is to propose novel civil aircraft cost parameters’ selection method and novel cost estimation approach for civil aircraft so as to effectively simulate or forecast civil aircraft cost under poor information and small sample.

Based on existent cost estimation indexes, this paper summarized civil aircraft research and manufacturing cost impact index system and adopted grey relational model to select most important impact factors. Consider civil aircrafts’ cost information could not be easily collected, the author must estimate their costs with limited sample and poor information. A combination model of GM (0, N) model and BP neural network algorithm is proposed. Both advantages of simulation of BP neural network algorithm and poor information generation of GM (0, N) were effectively combined. Then steps of combined model were given out. Finally, nine types of aircrafts were used to test the validity of proposed model. As comparing with the traditional multiple linear regression model and simple GM (0, N) model, results indicated that proposed model can do the work better.

Grey relational model can be applied for parameters’ selection and combined GM (0, N) model and BP neural network algorithm can estimate aircraft’s cost as well. Results show that novel combined model could get high forecasting accuracy.

Cost estimation is key problem in production management of civil aircraft. Effective cost management could promote competitiveness of aircraft manufacturing company. Proposed combined model can be applied for civil aircraft cost estimation. Similarly, it could be applied for other complex equipment cost estimation.

The paper succeeds in proposing grey relational model for cost parameters’ selection and constructing a combination model of GM (0, N) model and BP neural network algorithm. Algorithm of the proposed model was discussed and steps were given out.

The purpose of this paper is to seek to drive the modernization of the entire national economy and maintain in the long-term stability of the whole society; this paper proposes an improved model based on the first-order multivariable grey model [GM (1, N) model] for predicting the housing demand and solving the housing demand problem.

This paper proposes an improved model based on the first-order multivariable grey model [GM (1, N) model] for predicting the housing demand and solving the housing demand problem. First, a novel variable SW evaluation algorithm is proposed based on the sensitivity analysis, and then the grey relational analysis (GRA) algorithm is utilized to select influencing factors of the commodity housing market. Finally, the AWGM (1, N) model is established to predict the housing demand.

This paper selects seven factors to predict the housing demand and find out the order of grey relational ranked from large to small: the completed area of the commodity housing> the per capita housing area> the one-year lending rate> the nonagricultural population > GDP > average price of the commodity housing > per capita disposable income.

The model constructed in the paper can be effectively applied to the analysis and prediction of Chinese real estate market scientifically and reasonably.

The factors of the commodity housing market in Wuhan are considered as an example to analyze the sales area of the commodity housing from 2015 to 2017 and predict its trend from 2018 to 2019. The comparison between demand for the commodity housing actual value and one for model predicted value is capability to verify the effectiveness of the authors’ proposed algorithm.

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

The widespread application of traditional grey model (GM) in different academic fields such as electrical engineering, education, mechanical engineering and agriculture provided the authors with an incentive to conduct the present empirical research in an accounting field, in particular, auditing practice. In this regard, the purpose of this paper is to employ the nonlinear type of the original GM to forecast the drastically changed data on audit reports, primarily due to the fact that the linear nature of GM is unable to forecast nonlinear data precisely. In essence, this paper adds value to the strand of audit report literature by examining the impact of different financial ratios on auditors’ opinion and then forecasting audit reports by employing GMs.

The grey forecasting model is known as a system containing uncertain information presented by grey numbers, equations and matrices. The grey forecasting model is employed by using a differential equation in an uncertain system with limited data set which is suitable for smoothing discrete data. In addition, the analyses are conducted by applying a sample of top 50 listed companies on the Tehran Stock Exchange during 2011-2016.

The findings suggest that audit reports are most influenced by the current ratio and conversely, least influenced by the ratio of working capital turnover. Moreover, the authors argue that the Nash nonlinear grey Bernoulli model is more precise than the nonlinear grey Bernoulli model and GM in forecasting audit reports.

The current study may give more strength to stakeholders in order to analyse and forecast audit report.

Traditional statistical methods to study the financial performance of any industry have many barriers and limitations in terms of the statistical distribution of the financial ratios, and, in particular, it considers only its positive values of it. The purpose of this paper is to estimate the financial performance of 24 Indian life insurance companies for the period from 2013 to 2016 using Grey relational analysis (GRA) proposed by Deng (1982) that accommodates the negative values in the analysis.

Financial performance of 24 Indian life insurance companies for the years from 2013–2014 to 2015–2016 is examined using a total of 14 indicators from capital adequacy ratios, liquidity ratios, operating ratios and profitability ratios (PR). The methodology used is GRA to obtain the Grey grades to rank the performance indicators, where higher relational grade shows better financial performance, and a lower score depicts the scope for improving the performance.

The results rank the insurance companies according to their financial performance in which Shriram insurance stands first with higher relational grade score, followed by the companies like IDBI Insurance, Sahara Insurance and Life Insurance Corporation of India. The main finding is that PR which have negative values are playing a crucial role in determining the financial performance of Indian life insurance companies.

This study has far-reaching practical implications in twofold: first, for the Indian life insurance industry, they have to concentrate more on PR for better financial health and, second, for any financial performance analysis, ignoring negative value ratios produce biased inference and GRA can be used for better inference.

This study is the first attempt to evaluate the financial performance of Indian life insurance using the GRA methodology. The advantage of GRA is that there is no restrictions on the statistical distribution of the data and it also accommodates the negative values, whereas all the other traditional methods insist on the statistical distribution of data, and, more importantly, they cannot handle negative values in the performance analysis.

The present study aims to assess the potential effects of intellectual capital (IC) and disclosure of firms' affiliate transactions on contractual costs (CC).

The statistical population of the study includes 768 firm-year observations listed on the Tehran Stock Exchange during 2012–2017. According to Pulic's model, the authors divide IC into three components, such as human capital (HC), relational capital and structural capital (SC). CC is also measured by utilising two variables of board cash compensation and unexpected reward of managers.

The results show that there is a negative and significant relationship between HC and CC. In contrast, the authors find that relational capital and SC have a positive impact on CC. The authors’ further analyses also demonstrate that disclosure of transactions with affiliates has a negative effect on unexpected rewards of managers.

Since there is no conducted study, which discusses the relationship between IC and contractual cost, this paper might be considered the primary studies conducted in this line of literature, specifically in emerging markets. Moreover, to the best of the authors' knowledge, this is the first study investigating the potential impact of disclosure of selling and purchasing transactions, separately, on the director's unexpected reward.