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The purpose of this paper is to study the parameters' properties of GM(n, h) model on the basis of multiple transformation and the relationship of GM(n, h) model and other grey models.

Multiple transformation property of parameters is important to construct a grey model. However, there is no research on the property of GM(n, h) model, therefore it is meaningful to study the relationship between GM(n, h) model and other grey models.

The multiple transformation property of parameters of GM(n, h) model is recognized. The parameters' value is dependent on multiple transformation value. The values of simulative and predicative are only dependent to the multiple transformation of the main variable and independent to other variables.

The properties of other grey models could be obtained by analyzing the property of GM(n, h) model.

It is a very useful result for constructing a grey model.

This paper discusses multiple transformation property of GM(n, h) model and the relationship between the GM(n, h) model and other grey models. These grey models are put into a common model and the affections that parameters' multiple transformation caused to the model are studied.

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 construct a novel GM(0, N) model based on grey number sequences and to solve the problem of cost forecasting of commercial aircraft which puzzled managers, especially the factors of cost with uncertain information.

Based on the definition of traditional GM(0, N) model, the paper considers the limited information and knowledge, and the algorithm of grey numbers with greyness and kernel was designed. A novel GM(0, N) model based on grey number sequences, named the IN‐GM(0, N) model, is proposed according to the definition of the grey numbers algorithm. The steps of the proposed model are then given. Finally, a case of domestic commercial aircrafts is developed as an example, based on information gathering and model calculating.

The results of this research indicate that the IN‐GM(0,N) model is effective in cost calculating, providing reliable technical support for cost estimation of large‐scale complex equipment including commercial aircraft.

Cost forecasting of commercial aircraft can be solved effectively and the model can also be utilized to predicate other products.

The paper succeeds in constructing a novel grey forecasting model. This work contributes significantly to improving grey forecasting theory and to undoubtedly propose more novel grey forecasting models.

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

The purpose of this paper is to study a new approach by combining a multilayer perceptron neural network (MLPNN) algorithm with a GM(1, N) model in order to estimate the development cost of a new type of aircraft.

First, data about developing costs and their influencing factors were collected for several types of Boeing and Airbus aircraft. Second, a GM(1, N) model was constructed to simulate development costs for a civil aircraft. Then, an MLPNN algorithm was added to optimize and revise the simulative and forecasting values. Finally, a combined approach, using both a GM(1, N) model and an MLPNN algorithm was adopted to forecast development costs for new civil aircraft.

The results show that the proposed approach could do the work of cost estimation for new types of aircraft. Rather than using a single model, the combined approach could improve simulative and forecasting accuracy.

Scientific cost estimation could improve management efficiency and promote the success of a new type of civil aircraft development. Considering that China’s civil aircraft research and development is at its very beginning stages, only very limited data could be collected. The development costs for civil aircraft are affected by a series of factors. The approach outlined by this paper could be applied to development cost estimations in China’s civil aircraft industry.

The paper has succeeded by constructing a cost estimation index system and proposing a novel combined cost estimation approach comprised of a GM(1, N) model and an MLPNN. It has undoubtedly contributed to improving the accuracy of cost estimations.

This paper attempts to establish the grey GM(0,N) estimation model of the soil organic matter content spectral inversion under the uncertainties between soil organic matter contents and spectral characteristics and the theory of grey system.

At first, based on the uncertainty of the relationship between the soil organic matter content and spectral characteristics, using the ordered grey accumulation generation and grey GM(0, N) model to establish hyper‐spectral grey estimation model of soil organic matter content. Second, the presented model is used to estimate soil organic matter of Hengshan County in Shanxi province in the last part of the paper.

The results are convincing: not only that soil organic matter content spectral inversion grey GM(0, N) model based on the ordered grey accumulation generation theory is valid, but also the model's prediction accuracy is higher, with the sample's average prediction accuracy being 93.662 per cent.

The method exposed in the paper can be used on soil organic matter content hyper‐spectral inversion and even for other similar forecast problems.

The paper succeeds in realising both prediction pattern and application of soil organic matter content hyper‐spectral inversion by using the newest developed theories: grey GM(0, N) model based on the ordered grey accumulation generation.

The purpose of this paper is to address and overcome the problem that a single prediction model cannot accurately fit a data sequence with large fluctuations.

Initially, the grey linear regression combination model was put forward. The Discrete Grey Model (DGM)(1,1) model and the multiple linear regression model were then combined using the entropy weight method. The grain yield from 2010 to 2015 was forecasted using DGM(1,1), a multiple linear regression model, the combined model and a GM(1,N) model. The predicted values were then compared against the actual values.

The results reveal that the combination model used in this paper offers greater simulation precision. The combination model can be applied to the series with fluctuations and the weights of influencing factors in the model can be objectively evaluated. The simulation accuracy of GM(1,N) model fluctuates greatly in this prediction.

The combined model adopted in this paper can be applied to grain forecasting to improve the accuracy of grain prediction. This is important as data on grain yield are typically characterised by large fluctuation and some information is often missed.

This paper puts the grey linear regression combination model which combines the DGM(1,1) model and the multiple linear regression model using the entropy weight method to determine the results weighting of the two models. It is intended that prediction accuracy can be improved through the combination of models used within this paper.

The purpose of this paper is to propose a prediction model to predict the cost of complex products with lack of data. The cost estimating is one of the key elements of arguments around technological economy and investment decision‐making process of complex product.

A complex product has many characteristics, such as complex structure, large investment, high risk and it usually falls into small‐batch‐production category. Its cost estimation samples are small and cost data are very limited. Based on the characteristics of complex product and cost estimating, this paper introduces performance parameters sequence of associated known data, establishes an N‐GM (0, N) model of characteristic sequence with straddle missing data.

On the basis of the known key performance parameter sequence, N‐GM (0, N) model is used to predict the grey interval of overall cost vacancy data. Overall cost vacancy data is whitened by sorting reference sequence and realizing complex product overall cost estimation.

The method introduced in the paper can be used to solve practical problems, especially cost prediction of complex products with poor data. The model is also applied on the overall cost and the key component cost estimation of similar but different complex products. Moreover, it provides potential theoretical support for the development of complex product industry in the future.

In this paper, the complex product, which now plays a strategic industrial role in China, is systematically studied by utilizing a new methodology based on grey systems, especially the cost evaluation of the complex product. The use of grey correlation analysis in screening control key item index of complex product cost, the overall cost sequence of the complex product as related sequence and sorting reference sequence, the paper predicts and whitens vacant key item index, obtaining the key item cost index of complex product.

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.

The purpose of this paper is to propose an economic cybernetics model based on the grey differential equation GM(1,N) for China's high-tech industries and provide the necessary support to assist high-tech industries management departments with their policy making.

Based on the principle of grey differential equation GM(1,N), the grey differential equations of five high-tech industries in China are established using the net fixed assets, labor quantity and patent application quantity as cybernetics variables. After the discretization and first-order subtraction reduction to the simultaneous equation of the five grey models, a linear cybernetics model is resulted in. The structure parameters in the cybernetics system show explicit economic significance and can be identified through least square principle. At last, the actual data in 2004-2010 are introduced to empirically analyze the high-tech industrial system in China.

The cybernetics system for China's high-tech industries are stable, observable, and controllable. On the whole, China's high-tech industries show higher output coefficients of the patent application quantity than those of net fixed assets and labor quantity. This suggests that China's industry development mainly depends on technological innovation rather than capital or labor inputs. It is expected that the total output value of China's high-tech industries will grow at an average annual rate of 15 percent in 2011-2015, with contributions of pharmaceuticals, aircraft and spacecraft, electronic and telecommunication equipments, computers and office equipments, medical equipments and meters by 21, 16, 13, 10, and 28 percent, respectively. In addition, pharmaceuticals, as well as medical equipments and meters, present upward proportions in the gross of Chinese high-tech industries significantly. Electronic and telecommunication equipments, plus computers and office equipments exhibit an obvious decreasing proportion. The proportion of the output value of aircraft and spacecraft is basically stable.

Empirical analysis results are helpful for related management departments to formulate reasonable industrial policies to keep the sustained and stable development of the high-tech industries in China.

Based on the grey differential equation GM(1,N), this research puts forward an economic cybernetics model for the high-tech industries in China. This model is applicable to the economic system with small sample data set.