A novel grey relational model based on grey number sequences

2011 ◽  
Vol 1 (2) ◽  
pp. 117-128 ◽  
Author(s):  
Nai‐ming Xie ◽  
Si‐feng Liu
Keyword(s):  
Relational Model ◽  
Model Based ◽  
Number Sequences ◽  
Grey Number ◽  
Grey Relational

Grey Correlation Model Based on Diatom Indices Evaluating Water Quality of Longjiang River

2013 ◽  
Vol 448-453 ◽  
pp. 43-47 ◽  
Author(s):  
Xin Tang ◽  
De Suo Cai ◽  
Wen Ting Yao
Keyword(s):  
Water Quality ◽  
Water Quality Assessment ◽  
Quality Standard ◽  
Relational Model ◽  
Water Quality Standard ◽  
Diatom Index ◽  
Model Based ◽  
Diatom Indices ◽  
Grey Relational

In order to evaluate the water quality of Longjiang river comprehensively, diatoms of 15 sampling sites are collected to establish the Grey Relational Model based on three diatom indexesIPS, IBD and IDG. From the Cluster analysis of sampling sites and the box plot of diatom index, IBD is the best, then the IPS, the diatom index weights on water quality assessment are 0.637 for IBD, 0.2583 for IPS, 0.1074 for IDG respectively. Finally, by comparing the water quality standard level based on Grey Relational Model, it can be known that the water quality of most sampling sites is fine except that site No.1 and No.3 belong to III water quality standard. The result shows that it is more comprehensive and reasonable to use the Grey Relational Model based on diatom index rather than individual diatom index to assess water quality.

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.

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.

scholarly journals A new grey relational model based on discrete Fourier transform and its application on Chinese marine economic

2018 ◽  
Vol 1 (1) ◽  
pp. 79-100 ◽  
Author(s):  
Xuemei Li ◽  
Ya Zhang ◽  
Kedong Yin
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Relational Model ◽  
Relational Models ◽  
Content Type ◽  
Dynamic Correlation ◽  
Model Based ◽  
Cyclical Fluctuation ◽  
Grey Relational ◽  
Time Sequences

Purpose The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues. Design/methodology/approach Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA). Findings To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability. Originality/value DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

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.

Surface Image Edge Detection Algorithm Based on Grey Relational Analysis

2012 ◽  
Vol 461 ◽  
pp. 343-346 ◽  
Author(s):  
Gang Li ◽  
Ying Fang ◽  
Ya La Tong
Keyword(s):  
Edge Detection ◽  
Good Method ◽  
Detection Algorithm ◽  
Relational Model ◽  
Small Data ◽  
The Road ◽  
Image Edge Detection ◽  
Surface Image ◽  
Image Edge ◽  
Grey Relational

Automatic detection of pavement cracks is one of the very hot topics. For the characteristics of “small data, poor information” in the surface image processing, we construct ed a grey image relational model to characterize the local image edge feature, by selecting the appropriate threshold to extract the edge of appropriate level. Finally, simulation experiments show that the new algorithm can effectively improve the road edge detection results, and it is an effective good method worthy further study.

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