Table of Content

01 March 2020, Volume 32 Issue 1

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A Novel TODIM Method Based On General Grey Numbers And Grey Incidence Analysis Model

Peng Li, Liyong Huo, Ju Liu

2020, 32(1):  1-15. 

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 In the current study a novel TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) method has been proposed to solve multiple criteria decision making problems in which the decision matrix is characterised by general grey numbers. Firstly, a new axiom definition of distance measure is defined and two distance formulae are proposed. Later, a new standardized method for general grey numbers is put forward. Based on the distance formulae, a grey incidence method considering position weights using the idea of OWA operator is presented. Furthermore, a new approach to obtain the criteria weights using the grey incidence method is proposed. Moreover, a new TODIM method with general grey numbers, considering the bounded rationality of decision-maker is presented. Finally, a realistic case illustrates the effectiveness of the proposed methodology. 

Using Grey Model To Predict The Governance Indicators In China And India

Kaihe Shi, Ming Bai

2020, 32(1):  16-28. 

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To analyse the development of China and India, the governance indicators (including Voice and Accountability, Political Stability and Government Effectiveness, Regulatory Quality, Rule of Law, as well as Control of Corruption) in these two countries are forecasted by the fractional order accumulation grey number model, in the current study. The variation trend of six indicators will keep gentle growth or a slight decrease, except for the governance indicator of Control Corruption shows a substantial increase. Our results can provide references for policy makers, experts and investors.

A Generalized Grey Universal Approximation For Poor Data Discrete Nonlinear Systems#br#

Tie Wang

2020, 32(1):  29-37. 

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The approximation expression of discrete data can describe the system well and clearly. Traditional approximation methods require a lot of data, so they are not suitable for poor data discrete nonlinear systems. In order to overcome the shortcomings of traditional methods, a generalized grey universal approximation method for poor data discrete nonlinear systems was proposed. First, subdivide the range of the discrete system as needed. Second, build the grey possibility function as the basis function. Third, use the curve fitting method to determine the weight of the basis function. The results of simulation supported the effectiveness of the model.

Scaling Foreign-Service Premium Allowance Based On SWARA And GRA With Grey Numbers

Moses Olabhele Esangbedo, Sijun Bai

2020, 32(1):  38-58. 

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International companies need to compensate expatriates in relative proportions to the sacrifices they make to encourage them to accept overseas assignments in countries with harsh working conditions. The scaling of the foreign-service premium allowance problem is addressed as a multi-criteria decision-making problem. This paper presents a unique application of Grey System Theory to the compensation and benefit section of human-resource management. Firstly, this paper presents a hierarchical diagram to evaluate a company’s overseas branches for scaling the compensation of expatriates. Secondly, an unconventional hybrid method for group decision-making with uncertainty is presented. The hybrid method, Stepwise Weight Analysis Ratio Assessment weighting method and the Grey Relational Analysis with grey numbers, is applied to scale the foreign-service premium allowance and rank overseas branches of a company. The research results obtained are from a case study of the solutions to an international company, which was satisfying for both top management and staff union.

Credibility Evaluation For Small Sample Data Based On Grey System Theory And Cloud Mode

Jianmin Wang, Jinbo Wang

2020, 32(1):  59-77. 

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In the case of big data sample, data reliability could be evaluated easily by probability and some other methods. In engineering practice, the credibility assessment of small sample data without reference standard is often encountered, which is a hard problem. A method of credibility evaluation for small sample data based on grey system theory and cloud model is proposed. In accordance with the grey approaching correlation, the grey estimated value of small sample data is calculated. On the basis of grey estimated value, the parameters of mean, entropy and hyper entropy for cloud model can be calculated. Then the cloud model is built. Take advantage of the cloud model, amount of cloud drop data is produced around the data of the small sample. In the light of the confidence degree of cloud data, the credibility of each data for small sample data can be obtained. Finally, several simulations and analysis are conducted. The simulation results demonstrate the feasibility and effectiveness of the proposed method.

A Forecasting Framework Based On GM(1,1) Model And Long Short-Term Memory Network

Le Li, Gongyu Hou, Xiaoge Quan, Yajie Yang, Xiaoyun Ma, Wei Liu

2020, 32(1):  78-89. 

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As a basic model of the grey system theory, the GM(1,1) model has a very wide range of application, which uses the finite samples or poor information. One of its major drawbacks is the low precision in forecasting the long-term sequences. To solve this problem, the residual of the GM(1,1) is used to be optimized by introducing other algorithms which can greatly improve the overall prediction performance. This paper introduces the long short-time memory network to optimize the residuals of the GM(1,1), which can make full use of the nonlinear mapping and its mining ability for time series to achieve higher prediction accuracy. The chronological residual sequence of the GM(1,1) model is processed to generate a new time series that can regard as the initial sequence for long short-time memory network to train and predict the corrected residual. Based on the corrected residual model, the predicting value of the GM(1,1) model is added with the predicting value of the corrected residual sequence to get the ultimate forecasting value. The feasibility and accuracy are verified by one case which shows that the combined model of the GM(1,1) and LSTM network can get the better precision and make up for the defects of the traditional GM(1,1) in processing long complex time series. The application range of the GM (1,1) model is extended to some extent.

Fractional Order Accumulation Polynomial Time-Varying Parameters Discrete Grey Prediction Model And Its Application

Pumei Gao, Jun Zhan

2020, 32(1):  90-107. 

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The polynomial time-varying parameters discrete grey prediction model(PDGM (1,1,m) model) is a novel method to deal with the system that contains both exponential and polynomial trend. The PDGM (1,1,m) model can provide satisfactory modeling accuracy for a stable system. However, high-order PDGM (1,1,m) models are prone to overfitting and the prediction error increases significantly. Therefore the fractional order cumulative polynomial time-varying parameters discrete grey prediction model (FPDGM (1,1,r) model) is proposed in this paper. It is found that the perturbation bounds of the FPDGM (1,1,r) model are smaller than that of the PDGM (1,1,m) model by using the matrix disturbance theory. And the overfitting problem can be reduced well by the FPDGM (1,1,r) model. Finally, numerical example and actual cases show that the accuracy of the new model is higher than that of the traditional grey model. The practicability and validity of the model are further verified.

On Spectral Analysis And New Research Directions In Grey System Theory 

Sifeng Liu, Changhai Lin, Liangyan Tao, Saad Ahmed Javed, Zhigeng Fang, Yingjie Yang

2020, 32(1):  108-117. 

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Spectral analysis as a powerful mean to identify the characteristics of data series is introduced in this paper. The problems requiring further explorations in grey system theory are also identified. This includes discrimination of various factors of a data sequence in frequency domain, spectral analysis of various sequence operators, the synthesis axiom of degree of greyness for “multiplication” and “division” etc. Further, how to select and test a grey prediction model? How to select and test an inverse grey incidence analysis model? The test rules and criteria of grey clustering evaluation models, etc.

A Novel Grey Model With A Three-Parameter Background Value And Its Application In Forecasting Average Annual Water Consumption Per Capita In Urban Areas Along The Yangtze River Basin

Shuliang Li, Bo Zeng, Xin Ma, Dehai Zhang

2020, 32(1):  118-132. 

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The traditional grey models with two-parameters are always accompanied by the effect of extreme values in the raw sequence, which influences the accuracy of the simulation and prediction by grey models. This paper proposes a TPBVGM(1,1) model(three-parameters background values of the grey model with a single variable and a first order equation)by increasing the number of parameters in the background value. This novel model improves the smoothness of the background value and weakens the effects of extreme values in the raw sequence on the basis of proving that a two-parameter background value assignment is not reasonable. The objective of devising this model is to improve the accuracy of predictions. The TPBVGM(1,1) model is then applied to simulate and forecast the average water usage per person in the cities and towns along the Yangtze River basin; the simulation and prediction performance of the TPBVGM(1,1) model are then tested by comparison with the simulation and prediction results of traditional grey prediction models. The results show that the TPBVGM(1,1) model has a higher accuracy for simulation and prediction than the traditional grey prediction models. The results of the study provide a new research method for simulation and prediction with a grey system model.

Prediction Of Direct Economic Loss Caused By Marine Disasters Based On The Improved GM(1,1) Model

Yun Cao, Kedong Yin, Xuemei Li

2020, 32(1):  133-145. 

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Marine disasters seriously affect the economic and social development of China's coastal cities. Therefore, predicting the losses caused by marine disasters can assist earthquake prevention and disaster reduction departments in optimally preventing and reducing economic losses. However, due to the substandard state of the current marine disaster loss system, it is difficult to predict the potential losses that a marine disaster would cause accurately. The purpose of this paper is to propose an effective method for predicting the direct economic loss by marine disasters. A power buffer operator is used to process the original data before modeling, reducing the impact of system shock disturbance and the randomness of the data. This allows the disaster loss data to reflect the characteristics of the system better. In addition, the background value of the GM(1,1) model is reconstructed based on the Boolean formula and Newton combination interpolation, and the time-weighted least squares method is used to improve the GM(1,1) model to predict the direct economic loss by marine disasters. It is demonstrated that the improved GM(1,1) model can predict the direct economic loss caused by marine disasters. Compared with the traditional GM(1,1) model, the new grey prediction model greatly improves the prediction accuracy of the model. The original prediction error of 40.74% dropped to 6.64%, allowing for the accurate prediction of direct economic loss by marine disasters.