GIM(1) Model and its Application

2011 ◽  
Vol 219-220 ◽  
pp. 432-435
Author(s):  
Bin Zeng ◽  
Wu Jun Zeng
Keyword(s):  
System Application ◽  
Grey Model ◽  
Difference Quotient ◽  
Grey System ◽  
The Difference

Although the GM(1,1) model has been successfully adopted in various fields and has been demonstrated promising prospect. The paper adopts different form of grey model which is a supplement of the grey model and we call it GIM(1) model. On the analyzing the unequal GM(1,1) model the paper uses the difference quotient method to establish the unequal interval GIM(1) model. The examples prove the method in the paper is effective which improves the accuracy of the grey model. It provides an effective way for the grey system application.

GSM(1) Model and its Application

2011 ◽  
Vol 225-226 ◽  
pp. 1360-1363
Author(s):  
Bin Zeng ◽  
Wu Jun Zeng
Keyword(s):  
System Application ◽  
Original Data ◽  
Grey Model ◽  
Time Interval ◽  
Difference Quotient ◽  
Grey System ◽  
Effective Form ◽  
Adaptive Capability ◽  
The Right

Although the GM(1,1) model has been successfully adopted in various fields and has been demonstrated promising prospect. But the form of the GM(1,1) model is single and obviously is not suitable for all data with different character. In order to increase the adaptive capability some different forms of the grey model is needed to be established. The paper adopts combinatorial form instead of const in the right part of the grey equation which we call it GSM(1) model. GSM(1) model is one variable index serials function which contains more information in the equation and can find more complicated law between data. On the condition of the original data multiplying the time interval the paper introduces difference quotient into the equation and establishes the unequal GSM(1) model. The examples prove GSM(1) is an effective form to improve the accuracy of the grey model. It provides a new way for the grey system application.

Unequal Interval GM(1,1) Model of Weighted Coefficient Adjustment and its Application

2011 ◽  
Vol 219-220 ◽  
pp. 428-431 ◽  
Author(s):  
Bin Zeng ◽  
Lin Fang Li
Keyword(s):  
Fatigue Strength ◽  
System Application ◽  
Original Data ◽  
Forecasting Model ◽  
Time Interval ◽  
Difference Quotient ◽  
Grey System ◽  
Strength Data ◽  
Grey Forecasting ◽  
The Difference

Although the grey forecasting model has been successfully adopted in various fields and has been demonstrated prospected aspect. The paper makes the original data multiply the time interval to get the accumulated sequence and uses the difference quotient method to establish the unequal interval GM(1,1) model. In order to reduce the error the paper adopts the weighted coefficient to revise the background values. By fitting and predicting the fatigue strength data it proves the method in the paper is effective which improves the accuracy of the model. It provides an effective way for the grey system application.

Prediction of Technical Reserves Based on Grey Model — GM(1,1): Evidence from Non-life Egyptian Insurance Market

2019 ◽  
Vol 10 (9) ◽  
pp. 852-860
Author(s):  
Mahmoud Elsayed ◽  
◽  
Amr Soliman ◽  
Keyword(s):  
System Theory ◽  
Grey System Theory ◽  
Insurance Market ◽  
Grey Model ◽  
Loss Ratio ◽  
Grey System ◽  
Mathematical Technique ◽  
Supervisory Authority ◽  
Error Ratio ◽  
Using Data

Grey system theory is a mathematical technique used to predict data with known and unknown characteristics. The aim of our research is to forecast the future amount of technical reserves (outstanding claims reserve, loss ratio fluctuations reserve and unearned premiums reserve) up to 2029/2030. This study applies the Grey Model GM(1,1) using data obtained from the Egyptian Financial Supervisory Authority (EFSA) over the period from 2005/2006 to 2015/2016 for non-life Egyptian insurance market. We found that the predicted amounts of outstanding claims reserve and loss ratio fluctuations reserve are highly significant than the unearned premiums reserve according to the value of Posterior Error Ratio (PER).

scholarly journals Utilizing an Adaptive Grey Model for Short-Term Time Series Forecasting: A Case Study of Wafer-Level Packaging

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Che-Jung Chang ◽  
Der-Chiang Li ◽  
Wen-Li Dai ◽  
Chien-Chih Chen
Keyword(s):  
Semiconductor Manufacturing ◽  
Manufacturing System ◽  
Grey System Theory ◽  
Grey Model ◽  
Grey System ◽  
Wafer Level ◽  
Short Term ◽  
Packaging Process ◽  
Wafer Level Packaging

The wafer-level packaging process is an important technology used in semiconductor manufacturing, and how to effectively control this manufacturing system is thus an important issue for packaging firms. One way to aid in this process is to use a forecasting tool. However, the number of observations collected in the early stages of this process is usually too few to use with traditional forecasting techniques, and thus inaccurate results are obtained. One potential solution to this problem is the use of grey system theory, with its feature of small dataset modeling. This study thus uses the AGM(1,1) grey model to solve the problem of forecasting in the pilot run stage of the packaging process. The experimental results show that the grey approach is an appropriate and effective forecasting tool for use with small datasets and that it can be applied to improve the wafer-level packaging process.

scholarly journals Assessment of the Construction of a Climate Resilient City: An Empirical Study Based on the Difference in Differences Model

2021 ◽  
Vol 18 (4) ◽  
pp. 2082
Author(s):  
Zifeng Liang
Keyword(s):  
Significant Contribution ◽  
Evaluation Method ◽  
Regional Climate ◽  
Chinese Government ◽  
Infrastructure Development ◽  
Grey System ◽  
Difference In Differences ◽  
Climate Resilience ◽  
The Difference ◽  
The Impact

Facing climate risks has become a common problem for mankind and a topic of great importance for the Chinese government. To thoroughly implement the overall requirements for the construction of an ecological civilization and effectively improve the capacity of cities to adapt to climate change, China launched the pilot construction of “Climate Resilient Cities” in 2017. In this paper, 16 prefecture level cities in Anhui Province of China were selected as the research objects, and the multi-level grey system evaluation method was used to measure the climate resilience of these regions. We used the difference in differences method to evaluate the effect of the pilot policy of “Climate Resilient Cities.” The pilot policies of the “Climate Resilient Cities” showed a significant contribution to the regional climate resilience, and, after isolating the impact of other factors on the regional climate resilience, the pilot policies of the “Climate Resilient Cities” increased the climate resilience of the pilot cities by four percentage points. The pilot policies of the “Climate Resilient Cities” had a significant contribution to the urban infrastructure development and ecological space optimization, as well as non-significant impacts to the urban water security, emergency management capacity-building, and science and technology innovation initiatives.

Research and Application of Grey Predictive Model Based on Wavelet Analysis

2012 ◽  
Vol 170-173 ◽  
pp. 2912-2916
Author(s):  
Hai Ping Xiao ◽  
Lan Lan Chen ◽  
Yi Qiang Chen ◽  
Zhong Qun Guo
Keyword(s):  
System Theory ◽  
Wavelet Analysis ◽  
Predictive Model ◽  
Wavelet Transformation ◽  
Scientific Basis ◽  
Grey System Theory ◽  
Grey Model ◽  
Grey System ◽  
Predicting Model ◽  
Feasible Method

It is the scientific basis of instructing the project to produce and operate that the deformation is monitored, and the analysis and prediction in constructing and operating of project is one of the important jobs. In order to analyze and predict the deformation of the project more timely and accurately, the paper analyzed and established the feasibility of wavelet-grey predicting model on the basis of the grey system theory in modeling limitations and the characteristics of wavelet transformation. With the comparison of predictive datas in two kinds of models, the results show, the predictive datas of the wavelet-grey model are more accurately than grey model’s, and has achieved good results in prediction of the engineering, is a feasible method.

scholarly journals An Improved Nonequidistant Grey Model Based on Simpson Formula and Its Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhiming Hu ◽  
Chong Liu
Keyword(s):  
Prediction Accuracy ◽  
Prediction Models ◽  
Prediction Performance ◽  
Grey System Theory ◽  
Grey Model ◽  
Grey Prediction ◽  
Grey System ◽  
Proposed Model ◽  
Grey Models ◽  
High Prediction

Grey prediction models have been widely used in various fields of society due to their high prediction accuracy; accordingly, there exists a vast majority of grey models for equidistant sequences; however, limited research is focusing on nonequidistant sequence. The development of nonequidistant grey prediction models is very slow due to their complex modeling mechanism. In order to further expand the grey system theory, a new nonequidistant grey prediction model is established in this paper. To further improve the prediction accuracy of the NEGM (1, 1, t2) model, the background values of the improved nonequidistant grey model are optimized based on Simpson formula, which is abbreviated as INEGM (1, 1, t2). Meanwhile, to verify the validity of the proposed model, this model is applied in two real-world cases in comparison with three other benchmark models, and the modeling results are evaluated through several commonly used indicators. The results of two cases show that the INEGM (1, 1, t2) model has the best prediction performance among these competitive models.

On the Riemann Derivatives for Integrable Functions

1954 ◽  
Vol 6 ◽  
pp. 572-581 ◽  
Author(s):  
P. L. Butzer ◽  
W. Kozakiewicz
Keyword(s):  
Difference Quotient ◽  
Central Difference ◽  
Integrable Functions ◽  
The Difference ◽  
Image Position

The central difference of order s of the function f(x), Δs2hf(x), corresponding to a number h > 0, is defined inductively by the relations.If the limit of the difference quotientexists at the point x, it is called the sth Riemann derivative or the generalized sth derivative of fix) at the point x.

scholarly journals Grey Model Optimized by Particle Swarm Optimization for Data Analysis and Application of Multi-Sensors

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2503 ◽  
Author(s):  
Chenming Li ◽  
Hongmin Gao ◽  
Junlin Qiu ◽  
Yao Yang ◽  
Xiaoyu Qu ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Prediction Method ◽  
Temperature Data ◽  
Grey Model ◽  
Grey System ◽  
Swarm Optimization ◽  
Pumping Station ◽  
Unit Structure ◽  
Neural Network Prediction

Data on the effective operation of new pumping station is scarce, and the unit structure is complex, as the temperature changes of different parts of the unit are coupled with multiple factors. The multivariable grey system prediction model can effectively predict the multiple parameter change of a nonlinear system model by using a small amount of data, but the value of its q parameters greatly influences the prediction accuracy of the model. Therefore, the particle swarm optimization algorithm is used to optimize the q parameters and the multi-sensor temperature data of a pumping station unit is processed. Then, the change trends of the temperature data are analyzed and predicted. Comparing the results with the unoptimized multi-variable grey model and the BP neural network prediction method trained under insufficient data conditions, it is proved that the relative error of the multi-variable grey model after optimizing the q parameters is smaller.

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

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