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The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity.

The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model.

The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations.

The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged.

The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.

This paper aims to analyze general development trend of China’s population and to forecast China’s total population under the change of China’s family planning policy so as to measure shock disturbance effects on China’s population development.

China has been the most populous country for hundreds of years. And this state will be sustained in the forthcoming decade. Obviously, China is confronted with greater pressure on controlling total scale of population than any other country. Meanwhile, controlling population will be beneficial for not only China but also the whole world. This paper first analyzes general development trend of China’s population total amount, sex ratio and aging ratio. The mechanism for measurement of the impact effect of a policy shock disturbance is proposed. Linear regression model, exponential curve model and grey Verhulst model are adopted to test accuracy of simulation of China’s total population. Then considering the policy shock disturbance on population, discrete grey model, DGM (1, 1), and grey Verhulst model were adopted to measure how China’s one-child policy affected its total population between 1978 and 2015. And similarly, the grey Verhulst model and scenario analysis of economic developing level were further used to forecast the effect of adjustment from China’s one-child policy to two-child policy.

Results show that China has made an outstanding contribution toward controlling population; it was estimated that China prevented nearly 470 million births since the late 1970s to 2015. However, according to the forecast, with the adjustment of the one-child policy, the birth rate will be a little higher, China’s total population was estimated to reach 1,485.59 million in 2025. Although the scale of population will keep increasing, but it is tolerable for China and sex ratio and trend of aging will be relieved obviously.

The approach constructed in the paper can be used to measure the effect of population change under the policy shock disturbance. It can be used for other policy effect measurement problems under shock events’ disturbance.

The paper succeeded in studying the mechanism for the measurement of the post-impact effect of a policy and the effect of changes in China’s population following the revision of the one-child policy. The mechanism is useful for solving system forecasting problems and can contribute toward improving the grey decision-making models.

The purpose of this paper is to evaluate, analyse and select the best suppliers for Satrec Vitalait Milk Company, operating in Senegal, based on criteria obtained from economic, environmental and social dimensions of sustainable supply chain management, through the application of Deng’s grey relational analysis (GRA) model, absolute GRA model (ADGRA) and a novel second synthetic GRA (SSGRA) model, combined with one decision making under the uncertainty-based model, namely, the Hurwicz criteria.

The research adopts a new synthetic GRA model and highlights its reliability on small sample gathered from four senior experts of the company who administered a total number of 28 specialists operating in four departments of the company, through the employment of a self-administered questionnaire designed based on criteria identified from the literature that were refined via a Q-sort model.

The outcomes of the research methodology designated that all the selected five suppliers present a degree of attaining sustainability due to the fact that supplying unprocessed milk does not require the use of polluting methods for stocking and transportation. The undertaken study specifies that all the socio-environmental criteria play a crucial role in shaping the sustainability level of Satrec Vitalait’s suppliers and demonstrates the accuracy of the results obtained through the second synthetic degree of grey relation analysis for ranking the suppliers. Supplier 2 was found to be the best supplier for the company and, as result, a model for other suppliers to mimic.

Future researchers can replicate the GRA-based supply chain model proposed in the current study in different environments especially in the context of green supply chain. Also, in future the SSGRA model, while using the bidirectional ADGRA instead of the conventional ADGRA, should also be tested, especially when the data sequences associated with different supply chain parameters have inconsistent directions. Also, comparative analysis of SSGRA-based results with that of modern statistical methods like structural equation modelling can also be used for future explorations. Furthermore, the current study is built upon the data associated with the Satrec Vitalait Milk Company (Senegal); therefore, the findings should be generalised with caution.

The study can be seen as a first-stepping stone for gauging and selecting the best sustainable supplier for Satrec Vitalait using grey system theory. For purpose of attaining the research goal, the SSGRA was exploited as an innovative experimental approach to estimate relationships between criteria with regard to the sustainability level of the company’s suppliers. Under this scope, relationships between criteria themselves and their goal were depicted by Deng’s degree of GRA and AGRA, respectively. The research is innovative by means of the framework of its methodology and data analysis.

The purpose of this paper is to establish a group of grey prediction models and relative degree model to study the characteristics and trend of the logistics industry development in Henan province scientifically. The study results can provide references for the development policy of the logistics industry in Henan province.

The paper constructs grey prediction models and grey buffer operator models which are related to the distribution of logistics industry in Henan province, and selects prediction models by comparing model accuracy, and use them to forecast the development trend of logistics industry in future ten years of Henan province. Using the grey relative models, the paper analyses development dynamic and prospect which support the development of logistics industry, and provide some references for transferring the pattern of economic growth of Henan province, forming new economic growth point and formulating relevant policies. High prediction accuracy models are selected to forecast the future development trend of logistics industry in the next ten years.

Results show that the modern logistics industry in Henan province has been a steady growth in overall, the main growth points of the logistics industry development in Henan province are roadway miles (km), roadway (100 million tonnes/km), freight turnover (100 million tonnes/km) and waterway (100 million tonnes), the growth points for the future development of logistics industry in Henan province are the roadway freight volume, roadway passenger volume and waterway freight volume.

Regional economic competition has become an important index for measuring a country's economic development level. Logistics industry plays an important role in the regional economic development, such as promoting coordinated development of regional economy and upgrading industrial optimization, and playing a major role in industrial transfer. Hence, logistics industry, which is urgently needed to solve by the government, has become important forces for promoting the growth of economy and a basic pillar industries of regional economy.

The paper presents the systematic results of development prediction of modern logistics industry in Henan province and its dynamic analysis by using grey systems theory, not only to predict the trend of the development of the logistics industry, also to analyse the future development of logistics industry in the leading power factors.

The purpose of this paper is to propose a novel approach to improve prediction accuracy of grey power models including GM(1, 1) and grey Verhulst model.

The modified new models are proposed by optimizing the initial condition and model parameters. The new initial condition consists of the first item and the last item of a sequence generated by applying the first-order accumulative generation operator on the sequence of raw data.

It is shown that the newly modified grey power model is an extension of the previous optimized GM(1, 1) and grey Verhulst model. And the optimized initial condition reflected the principle of new information priority.

The result of a numerical example indicates that the modified grey model presented in this paper with better prediction performance.

The new initial condition are derived by weighted combination of the first item and the last item. The coefficients of weight obtained by the least square method.

The purpose of this paper is to improve the development of the Chinese traditional medicine (included the ethnic minority's medicine in China), it can raise the level of health for people, carry forward the culture of our nation, accelerate the economic development, promote social harmony and is very significant.

In this paper, the factor which influences the development of the Chinese traditional medicine in these areas of China is analysed by the method called the grey relational analysis and grey clustering analysis.

It is known that the comparative situation of each otherof the development of the Chinese traditional medicine in these areas. The causation is analysed.

The behavioural mechanisms information which is effected by the traditional Chinese medicine (included ethnic minority medicine) is incomplete. Its inherent meaning is not clear. So it is reasonable to use the method called the grey relational analysis grey clustering analysis to study. Analysing the causes and giving countermeasures according to the results could propose some suggestions for the further development of Chinese medicine (including the national medicine) industry.

The grey system theory was applied in medical management. The application of study results, the development of the Chinese traditional medicine (included the ethnic minority's medicine in China) is improved.

The purpose of this paper is to build a linear time-varying discrete Verhulst model (LTDVM), to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations.

The methodology of the paper is by the light of discrete thoughts and countdown to the original data sequence.

The research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.

The example analysis shows that LTDVM embodies simulation and prediction with high precision.

This paper is to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations. Meanwhile, the research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.

The mobile communication industry in China is vulnerable to competition, industry regulation, macroeconomy and so on, which leads to service income's volatility and non-stationarity. Traditional income prediction models fail to take account of these factors, thus resulting in a low precision. The purpose of this paper is to to set up a new mobile communication service income prediction model based on grey system theory to overcome the inconformity between traditional models and qualitative analysis.

At first, mobile telecommunication service income is divided into number of users (NU) and average revenue per user (ARPU) prediction, respectively. Then, grey buffer operators are introduced to preprocess the time series according to their features and tendencies to eliminate the effect of shock disturbance. As a result, two grey models based on GM(1, 1) are constructed to forecast NU and ARPU, and thus the service income is obtained. At last, a case on Zhujiang mobile communication company is studied. The result proves that the proposed method is not only more accurate, but also could discover the turning point of income.

The results are convincing: it is more effective and accurate to employ grey buffer operator theory to predict the mobile communication service income compared with other methods. Besides, this method is applicable to cases with less data samples and faster development.

It's common to come across a system with less data and poor information. At this case, the grey prediction method exposed in the paper can be used to forecast the future trend which will give the predictors advice to achieve fine outcomes. Buffer operators can reduce the effect of shock disturbance and the GM(1, 1) model has the advantages of exploiting information using only a couple of data.

Considering the fast development of China's mobile communication in recent years, only limited data can be acquired to predict the future, which will definitely reduce the prediction precision using traditional models. The paper succeeds in introducing GM(1, 1) model based on grey buffer operators into the income prediction and the outcome proves that it has higher prediction precision and extensive application.

The purpose of this paper is to discuss the interval forecasting, prediction interval and its reliability. When the predicted interval and its reliability are construction, the general rule which must satisfy is studied, grey wrapping band forecasting method is perfect.

A forecasting method puts forward a process of prediction interval. It also elaborates on the meaning of interval (the probability of the prediction interval including the real value of predicted variable). The general rule is abstracted and summarized by many forecasting cases. The general rule is discussed by axiomatic method.

The prediction interval is categorized into three types. Three axioms that construction predicted interval must satisfy are put forward. Grey wrapping band forecasting method is improved based on the proposed axioms.

Take the Shanghai composite index as the example, according to the K-line diagram from 4 January 2013 to 9 May 2013, the reliability of predicted rebound height of subsequent two or three trading day does not exceed the upper wrapping curve is 80 per cent. It is significant to understand the forecasting range correctly, build a reasonable range forecasting method and to apply grey wrapping band forecasting method correctly.

Grey wrapping band forecasting method is improved based on the proposed axioms.