MGM(1,m) model based on interval grey number sequence and its applications

2017 ◽  
Vol 7 (3) ◽  
pp. 310-319 ◽  
Author(s):  
Pingping Xiong ◽  
Yue Zhang ◽  
Bo Zeng ◽  
Tian-Xiang Yao
Keyword(s):  
Prediction Models ◽  
Development Trend ◽  
Upper And Lower Bounds ◽  
Number Sequence ◽  
Content Type ◽  
Model Based ◽  
Grey Forecasting ◽  
Number Sequences ◽  
Grey Number ◽  
Predicted Values

Purpose Aiming at the traditional multivariate grey forecasting model only considers the modelling of real numbers; therefore, the purpose of this paper is to construct an MGM(1, m) model based on the interval grey number sequences according to the grey modelling theory. Design/methodology/approach First, the multivariable grey number sequences are transformed into the kernel and grey radius sequences which are two feature sequences of interval grey number sequences. Then the MGM(1, m) model for kernel sequences and grey radius sequences are established, respectively. Finally, the simulation and prediction of the upper and lower bounds of the interval grey number sequences are realized by the reductive calculation of the predicted values of the kernel and grey radius. Findings The model is applied to the prediction of visibility and relative humidity, the identification factors of the haze. The results show that the model has high accuracy on the simulation and prediction of multivariable grey number sequences, which is reasonable and practical. Originality/value The main contribution of this paper is to propose a method to simulate and forecast the multivariable grey number sequence that is to establish the prediction models for the whitening sequences of multivariable grey number sequences which are kernel and grey radius sequences and extend the possibility boundary of kernel by grey radius. The model can reflect the development trend of multivariable grey number sequence accurately. When the grey information is continuously complemented, the multivariable grey number prediction model is transformed into the traditional MGM(1, m) model. Therefore, the MGM(1, m) model based on interval grey number sequence is the generalisation and expansion of the traditional MGM(1, m) model.

Forecasting smog in Beijing using a novel time-lag GM(1,N) model based on interval grey number sequences

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jia Shi ◽  
Pingping Xiong ◽  
Yingjie Yang ◽  
Beichen Quan
Keyword(s):  
Time Lag ◽  
Upper And Lower Bounds ◽  
Simulation Accuracy ◽  
Content Type ◽  
Model Based ◽  
Proposed Model ◽  
Lag Effect ◽  
Number Sequences ◽  
The Government ◽  
Grey Number

PurposeSmog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.Design/methodology/approachThis paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.FindingsIn order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.Practical implicationsThe proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.Originality/valueBased on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

A novel GM(1,N) model based on interval gray number and its application to research on smog pollution

Kybernetes ◽  
2019 ◽  
Vol 49 (3) ◽  
pp. 753-778
Author(s):  
Pingping Xiong ◽  
Zhiqing He ◽  
Shiting Chen ◽  
Mao Peng
Keyword(s):  
Prediction Model ◽  
Practical Significance ◽  
Upper And Lower Bounds ◽  
Gray Model ◽  
Number Sequence ◽  
Mathematical Methods ◽  
Public Attention ◽  
Content Type ◽  
Model Based ◽  
Definition Of

Purpose In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods. Design/methodology/approach This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness. Findings To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy. Originality/value This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

Development of a direct NGM(1,1) prediction model based on interval grey numbers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ye Li ◽  
Yuanping Ding ◽  
Yaqian Jing ◽  
Sandang Guo
Keyword(s):  
Genetic Algorithm ◽  
Markov Model ◽  
Prediction Model ◽  
Real Number ◽  
Content Type ◽  
Optimal Weight ◽  
Practical Applications ◽  
Number Sequences ◽  
Integral Development ◽  
Grey Number

PurposeThe purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.Design/methodology/approachA definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.FindingsThe interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.Practical implicationsUncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.Originality/valueThe main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

scholarly journals A Novel Linear Time-Varying GM(1,N) Model for Forecasting Haze: A Case Study of Beijing, China

2019 ◽  
Vol 11 (14) ◽  
pp. 3832 ◽  
Author(s):  
Pingping Xiong ◽  
Jia Shi ◽  
Lingling Pei ◽  
Song Ding
Keyword(s):  
Linear Time ◽  
Dynamic Change ◽  
Time Varying ◽  
The Novel ◽  
Model Based ◽  
Number Sequences ◽  
The Government ◽  
Grey Number ◽  
Beijing China

Haze is the greatest challenge facing China’s sustainable development, and it seriously affects China’s economy, society, ecology and human health. Based on the uncertainty and suddenness of haze, this paper proposes a novel linear time-varying grey model (GM)(1,N) based on interval grey number sequences. Because the original GM(1,N) model based on interval grey number sequences has constant parameters, it neglects the dynamic change characteristics of parameters over time. Therefore, this novel linear time-varying GM(1,N) model, based on interval grey number sequences, is established on the basis of the original GM(1,N) model by introducing a linear time polynomial. To verify the validity and practicability of this model, this paper selects the data of PM10, SO2 and NO2 concentrations in Beijing, China, from 2008 to 2018, to establish a linear time-varying GM(1,3) model based on interval grey number sequences, and the prediction results are compared with the original GM(1,3) model. The result indicates that the prediction effect of the novel model is better than that of the original model. Finally, this model is applied to forecast PM10 concentration for 2019 to 2021 in Beijing, and the forecast is made to provide a reference for the government to carry out haze control.

Grey target decision-making model of interval grey number based on cone volume

2017 ◽  
Vol 7 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Lizhen Wang ◽  
Wuyong Qian
Keyword(s):  
Decision Making ◽  
Entropy Method ◽  
Maximal Entropy ◽  
Information Distortion ◽  
Content Type ◽  
Model Based ◽  
Proposed Model ◽  
Grey Number ◽  
Decision Making Model ◽  
The Impact

Purpose The purpose of this paper is to propose a grey target decision model based on cobweb area in order to overcome the effect and influence from the extreme value of the index on the decision result. However, it does not take into account the impact of the correlation between indicators on the angle of the index, and produce a certain degree decision information distortion as a result of the equal angle between the indicators. In order to solve the above problems, a novel grey decision-making model based on cone volume is proposed. Design/methodology/approach In this paper, the model uses the whitening weight function to whiten the interval grey number, and the Delphi method and the maximal entropy method are exploited to integrate the weight of the index. On the basis of this, the center of the bull’s eye, the weight and the index value are constructed as the center circle, the radius, and the high cone, respectively. The scheme is selected by the volume of the cone, the decision is made according to the order relation, and the example is utilized to prove and analyze the validity of the proposed model. Findings The results show that the proposed model can well improve the traditional grey target decision-making model from the modeling object and modeling method. Practical implications The method exposed in the paper can be used to deal with the grey target decision-making problems which characteristics are multi-indexes, and the attribute values are interval grey numbers. Originality/value The paper succeeds in overcoming the disadvantages of grey target decision making based on the target center distance and the cobweb area.

Analysis on the related factors of China's technological innovation ability using greyness relational degree

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Li Li ◽  
Xican Li
Keyword(s):  
Real Number ◽  
Technological Innovation ◽  
Number Sequence ◽  
Related Factors ◽  
Content Type ◽  
Grey Relational Degree ◽  
Relational Degree ◽  
Innovation Ability ◽  
Grey Number ◽  
Grey Relational

PurposeIn order to make grey relational analysis applicable to the interval grey number, this paper discusses the model of grey relational degree of the interval grey number and uses it to analyze the related factors of China's technological innovation ability.Design/methodology/approachFirst, this paper gives the definitions of the lower bound domain, the value domain, the upper bound domain of interval grey number and the generalized measure and the generalized greyness of interval grey number. Then, based on the grey relational theory, this paper proposes the model of greyness relational degree of the interval grey number and analyzes its relationship with the classical grey relational degree. Finally, the model of greyness relational degree is applied to analyze the related factors of China's technological innovation ability.FindingsThe results show that the model of greyness relational degree has strict theoretical basis, convenient calculation and easy programming and can be applied to the grey number sequence, real number sequence and grey number and real number coexisting sequence. The relational order of the four related factors of China's technological innovation ability is research and development (R&D) expenditure, R&D personnel, university student number and public library number, and it is in line with the reality.Practical implicationsThe results show that the sequence values of greyness relational degree have large discreteness, and it is feasible and effective to analyze the related factors of China's technological innovation ability.Originality/valueThe paper succeeds in realizing both the model of greyness relational degree of interval grey number with unvalued information distribution and the order of related factors of China's technological innovation ability.

A time-varying grey Riccati model based on interval grey numbers for China's clean energy generation predicting

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sandang Guo ◽  
Yaqian Jing
Keyword(s):  
Clean Energy ◽  
Energy Generation ◽  
Random Disturbance ◽  
Time Varying ◽  
The Novel ◽  
Content Type ◽  
Time Varying Parameter ◽  
Number Sequences ◽  
Disturbance Term ◽  
Grey Number

PurposeIn order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.Design/methodology/approachBy combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.FindingsBased on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.Practical implicationsDue to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.Originality/valueThe main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

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