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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.

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.

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.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.

The purpose of this paper is to clarify several commonly used quality cost models based on Juran’s characteristic curve. Through mathematical deduction, the lowest point of quality cost and the lowest level of quality level (often depicted by qualification rate) can be obtained. This paper also aims to introduce a new prediction model, namely discrete grey model (DGM), to forecast the changing trend of quality cost.

This paper comes to the conclusion by means of mathematical deduction. To make it more clear, the authors get the lowest quality level and the lowest quality cost by taking the derivative of the equation of quality cost and quality level. By introducing the weakening buffer operator, the authors can significantly improve the prediction accuracy of DGM.

This paper demonstrates that DGM can be used to forecast quality cost based on Juran’s cost characteristic curve, especially when the authors do not have much information or the sample capacity is rather small. When operated by practical weakening buffer operator, the randomness of time series can be obviously weakened and the prediction accuracy can be significantly improved.

This paper uses a real case from a literature to verify the validity of discrete grey forecasting model, getting the conclusion that there is a certain degree of feasibility and rationality of DGM to forecast the variation tendency of quality cost.

This paper perfects the theory of quality cost based on Juran’s characteristic curve and expands the scope of application 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 present a new model which combines the non-equidistant GM(1,1) model with GCHM_WBO (generalized contra-harmonic mean (GCHM); weakening buffer operator (WBO)). The authors use the model to solve the deadlock that for a large number of non-equidistant corrosion rate, it is difficult to establish a reasonable prediction model and improve the prediction accuracy.

This research consists of three parts: non-equidistant GM(1,1) model, GCHM_WBO operator, and the optimization of morphing parameter (contained in GCHM, control the intensity of the weakening operator). The methodology is explained as follows. First, the authors built a non-equidistant GM(1,1) model with GCHM_WBO weakened data, of which morphing parameter was randomly selected. Next, the authors calculated the error between prediction data of model and the real data, and adjusted the morphing parameter according to the error and property of GCHM. Then, the authors generated a new non-equidistant GM(1,1) based on new morphing parameter, and repeated the previous step until the termination condition was satisfied. Finally, the model with appropriate morphing parameter was used to implement the prediction of new data.

This paper finds a property of GCHM, which is a monotonic increasing function of morphing parameter in some specific conditions. Based on the property and the fixed point axiom of WBO, an algorithm was designed to search an appropriate morphing parameter. The appropriate morphing parameter was implemented for the purpose of improving the accuracy of the model. The model was applied to predict the corrosion rate of six steels at Guangzhou experimental station. The results showed that the proposed method can get more accuracy in prediction capability compared to the models with the original data and AWBO weakened data. The method is applicable to long-term forecasts in case of data scarcity.

Corrosion will cause huge economic loss to a country; therefore, it is important to judge the remaining useful life of a material or equipment; the foundation for judgement of which is the prediction of material corrosion rate. However, the prediction of corrosion rate is very difficult because of corrosion data’s features, such as small sample size, non-equidistant, etc. The proposed method can be used to implement long-term forecast of corrosion data with only one sample and non-equidistant samples.

This paper presented a model which combines the non-equidistant GM(1,1) model with GCHM_WBO to handle the problem of long-term forecasting of corrosion data. In the modelling process, the proposed morphing parameter searched through algorithm can improve the prediction accuracy of the model. Therefore, the model can provide effective and reliable result when data are of a small sample size and non-equidistant.

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.