A REPAIRABLE SYSTEM MODELLING: COMBINING GREY SYSTEM THEORY WITH INTERVAL-VALUED FUZZY SET THEORY

2005 ◽  
Vol 12 (03) ◽  
pp. 241-266 ◽  
Author(s):  
R. GUO
Keyword(s):  
System Theory ◽  
Fuzzy Sets ◽  
Underlying Mechanism ◽  
Grey System Theory ◽  
Small Sample ◽  
System Modelling ◽  
Repairable System ◽  
Type I ◽  
Grey System ◽  
Interval Valued

A fundamental but impossible to be addressed problem in repairable system modelling is how to estimate the system repair improvement (or damage) effects because of the large-sample requirements from the standard statistical inference theory. On the other hand, repairable system operating and maintenance data are often imprecise and vague and therefore Type I fuzzy sets defined by point-wise membership functions are often used for the modelling repairable systems. However, it is more logical and natural to argue that Type II fuzzy sets defined by interval-valued membership function, called interval-valued fuzzy sets (IVFS), should be used in characterizing the underlying mechanism of repairable system. In this paper, we explore a small-sample based GM(1,1) modelling approach rooted in the grey system theory to extract the system intrinsic functioning times from the seemly lawless functioning-failure time records and thus to estimate the repair improvement (damage) effects. We further explore the role of interval-valued fuzzy sets theory in the analysis of the system underlying mechanism. We develop a framework of the GM(1,1)-IVFS mixed reliability analysis and illustrate our idea by an industrial example.

Research on Duration Prediction of the Coupled Task Set Based on the Grey System Theory

2012 ◽  
Vol 220-223 ◽  
pp. 169-173
Author(s):  
Peng Jia ◽  
Qi Gao ◽  
Rong Zhen Xu ◽  
Xiao Chen Zheng ◽  
Gang Liu
Keyword(s):  
System Theory ◽  
Prediction Model ◽  
Grey System Theory ◽  
Small Sample ◽  
Practical Application ◽  
Grey System ◽  
Task Set ◽  
Posterior Variance ◽  
Duration Prediction

In order to solve the problem of duration predicting in the project with poor information, small sample and uncertainty, a method based on grey system theory is put forward to predicting the duration of the coupled task set. A grey duration prediction model GM(1,1) is built, and the accuracy of the model is tested through residual, degree of incidence and posterior variance. Finally, the feasibility of the prediction model is verified by a practical application case.

scholarly journals Time-Delayed Polynomial Grey System Model with the Fractional Order Accumulation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Lin Chen ◽  
Zhibin Liu ◽  
Nannan Ma
Keyword(s):  
System Theory ◽  
Fractional Order ◽  
Grey System Theory ◽  
Small Sample ◽  
System Model ◽  
Grey Prediction ◽  
Grey System ◽  
Forecasting Models ◽  
New Information ◽  
Grey System Model

In this work, a novel time-delayed polynomial grey prediction model with the fractional order accumulation is put forward, which is abbreviated as TDPFOGM(1,1), based on the new grey system theory to predict the small sample in comparison with the existing forecasting models. The new model takes into account the nonhomogeneous term and the priority of new information can be better reflected in the in-sample model. The data in this paper all come from the existing literatures. The results demonstrate that the TDPFOGM(1,1) model outperforms the TDPGM(1,1) and FOGM(1,1) model.

scholarly journals Prediction Method of Asphalt Pavement Performance and Corrosion Based on Grey System Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Ding-bang Zhang ◽  
Xin Li ◽  
Yi Zhang ◽  
Hang Zhang
Keyword(s):  
System Theory ◽  
Asphalt Pavement ◽  
Prediction Equation ◽  
Grey System Theory ◽  
Small Sample ◽  
Monitoring Data ◽  
Pavement Performance ◽  
Skid Resistance ◽  
Grey System ◽  
Absolute Correlation

The Grey system theory is a new mathematical method to predict data changes in the poor data integrity. As a branch of Grey system theory, the GM (1, 1) model is widely used because only small sample data and simple calculations are needed in prediction of engineering project. It is a critical problem to effectively predict the performance and corrosion of asphalt pavement of highway construction due to the inadequacy of highway performance monitoring data. The smoothness, rut, and pavement skid resistance are three important indexes to evaluate the performance and corrosion of asphalt pavement. This paper has established the prediction model and derived prediction equation of asphalt pavement performance according to the GM (1, 1) model method and then listed the calculation equation of residual and the gray absolute correlation degree. Based on the experience of constructed Dalian-Guangzhou expressway in China, the vectors “a” and “b” in the prediction equation of smoothness, rut, and pavement skid resistance have been calculated by using the original monitoring data. The field monitoring data are compared with the predictive data for residual and the gray absolute correlation. The results reveal that the predicted data of the smoothness, rut, and skid resistance are mostly consistent with the monitoring data, the biggest residual of the above three indexes is smaller than 8.09%, and the gray absolute correlation degrees all exceed 0.9, which means the accuracy of the predicted equation is excellent. The calculation method based on GM (1, 1) model can effectively predict the changing performance index of asphalt pavement.

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).

Application of Grey System Theory to tree growth prediction

2000 ◽  
Vol 11 (1) ◽  
pp. 34-36 ◽  
Author(s):  
Wang Jing ◽  
Hou Yuesong ◽  
Li Weilin ◽  
Cheng Wenhui
Keyword(s):  
System Theory ◽  
Tree Growth ◽  
Grey System Theory ◽  
Grey System ◽  
Growth Prediction

Grey-based model for forecasting Mauritius international tourism from different regions

2017 ◽  
Vol 7 (2) ◽  
pp. 259-271 ◽  
Author(s):  
Medha Pirthee
Keyword(s):  
System Theory ◽  
Grey System Theory ◽  
International Tourism ◽  
Grey System ◽  
Private Companies ◽  
Content Type ◽  
System Models ◽  
Economic Decision Making ◽  
Tourism Sector ◽  
The Government

Purpose The purpose of this paper is to understand the trend and forecast the number of tourists from different regions of the world to Mauritius. Design/methodology/approach The paper adopts two grey system models, the even model GM(1,1) and the non-homogeneous discrete grey model (NDGM), to forecast the total number of international tourism to Mauritius and its structure from different regions tourist arrivals to Mauritius for the next three years. Grey system theory models were used to account for uncertainties and the dynamism of the tourism sector environment. The two models were applied as a comparison to obtain more reliable forecasting figures. Findings The results demonstrate that both of the grey system models can be successfully applied with high accuracy for Mauritian tourism prediction, and also the number of tourist arrivals to Mauritius shows a continued augmentation for the upcoming years. Practical implications Forecasting is meaningful since the Government of Mauritius, private companies or any concerned authority can adopt the forecasting methods exposed in this paper for the development of the tourism sector through managerial and economic decision making. Originality/value Mauritius is a charming travel destination. Through this paper, it can be seen that future tourism travel to Mauritius has been successfully predicted based on previous data. Moreover, it seems that the grey system theory models have not been utilised yet as forecasting tools for the tourism sector of Mauritius as opposed to other countries such as China and Taiwan.

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