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Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to analyze the cause of increase in the simulation accuracy of the buffer operator.

This paper probed into the modeling mechanism of several typical buffer operators such as the arithmetic buffer operators, the buffer operators with monotonic function and weighted buffer operators. The paper also gives an example of the buffer operator sequence.

The results indicate that after applying an infinite buffer operator, whether the authors adopt a weakening buffer operator or a strengthen buffer operator, the raw sequence can be changed into a constant sequence. Because the discrete GM(1,1) model can completely simulate constant sequence, the simulation accuracy is 100 percent. Because the discrete GM(1,1) model is the accurate form of the GM(1,1) model, after applying an infinite buffer operator, the GM(1,1) model can have a very high simulation accuracy. The buffer operator model can increase the simulation accuracy of both the GM(1,1) model and the discrete GM(1,1) model.

The paper analyses the cause of increasing simulation accuracy of the buffer operator model. The paper may indicate that possible results can be studied in the future. All the buffer operator models have similar properties. After applying an infinite buffer operator, the raw sequence can be changed into a constant sequence. A fixed-point axiom may be the basic cause.

The purpose of this paper is to perfect the axiom systems of buffer operator via adding the axiom of invariable trend.

Based on the three axioms of buffer operator, for any given data sequence of system behavior and any set of data satisfying the axiom of fixed point, it is proved that there always exists a buffer operator satisfying that the set of data is the buffer sequence of the given data sequence, and a specific constructor method of buffer operator is provided. Finally, the axiom of invariable trend is proposed to add in the axiom systems of buffer operator.

The results are convincing that although the raw sequence suffered from certain disturbance may be enlarged or reduced, the trend is in line with the original law. All predictions must be on the premise of this trend to forecast, or prediction will be considered invalid.

The method exposed in the paper can be used to construct a specific buffer operator between two sequences satisfying the axiom of fixed point.

The paper succeeds in providing a kind of universal constructor method for buffer operator, and adding the axiom of invariable trend to perfect the axiom systems of buffer operator and ensure the consistency of variation trend between the predicted values and the actual values.

According to the basic principle of grey system and third axiom buffer operator, aiming at the problem of disturbance, some new weakening buffer operators are established by analytical skills in the process of prediction. The problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences is resolved effectively. An example shows that the kind of new weakening buffer operators increase the forecast precision of data forecast model remarkably. The aim of this paper is to attempt to resolve the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences.

In view of the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences, according to the basic principle of grey system and third axiom buffer operator, some new weakening buffer operators are established by analytical skills. As an example, the kind of new weakening buffer operators can increase the forecast precision of data forecast model remarkably.

The results show that the new weakening buffer operators can increase the forecast precision of data forecast model remarkably.

The new weakening buffer operators exposed in the paper can be used to resolve the problem of some contradictions between quantitative analysis and qualitative analysis existing in pretreatment for vibration data sequences and increase the forecast precision of data forecast model remarkably.

The paper succeeds in increasing the forecast precision of data forecast model remarkably.

The purpose of this paper is to solve the problem existing in the forecast of impact disturbance grey system.

Under the axiomatic system of buffer operator in grey system theory, a novel kind of buffer operators with variable weight λ based on the principle of average tempo of time sequence and using new information is proposed. The optimization solution for variable weight λ is obtained by using genetic algorithm. It is proved that the new buffer operators are effective.

The results show that the new buffer operators accord with the buffer operator's three axioms and the monotonicity non‐variable axiom. It is proved theoretically and in practice that the new buffer operators are more useful than other buffer operators in grey modeling for sequence with impact disturbance.

The novel buffer operators can reduce the randomness of grey sequence distorted by impact factors, and the forecast accuracy of a model which is built through the process with a novel buffer operator is significantly increased.

The paper succeeds in constructing two novel buffer operators with variable weight and the properties of novel operators are studied. The method to solve optimization value of weight is proposed. The method widens the scope of grey model application.

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 present the terms of sequence operators and grey data mining.

The definitions of basic terms about sequence operators and grey data mining are presented one by one.

The reader could know the basic explanation about the important terms about sequence operators and grey data mining from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

The purpose of this paper is to predict the main economic indices of online shopping in China.

A fractional order weakening buffer operator (WBO) for the GM(1,1) model is put forward in order to solve the problem of limited nonlinear data. The order number of WBO can adjust in line with the scenario.

The experimental results indicate that the proposed method can consider the scenario and obtain more accurate forecasting results.

This study found that the slowdown of growth trend after the previous high speed expansion period will continue, and the online shopping sellers should make more efforts to develop potential consumers to increase its turnover.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

One of the difficulties experienced in applications of exponential prediction models of time series is resolved by introducing sequence operators. This approach is different from all known modelings of time series and regression analysis. Also, discontinuities (or outliers), appearing in a given time series, can be naturally absorbed by applying sequence operators. This end is important since, in terms of predictions, outliers or discontinuities in the data might signal major changes in the pattern of the time series data.

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.