Table of Content

01 February 2024, Volume 36 Issue 1

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Memorabilia of the Establishment and Development of Grey System Theory 

Sifeng Liu, Liangyan Tao, Wei Tang

2024, 36(1):  1-3. 

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This article summarizes and records important historical events in the establishment and 40 year development process of continuing innovation and dissemination of grey system theory, providing reference for scholars who pay attention to the evolution laws of grey system theory, a new branch of uncertainty system research, as well as colleagues engaged in grey system theory research. If there are any important omissions, we sincerely welcome readers to supplement and improve. 

Modeling and Predicting the Socio-Economic Performance of Countries Using Grey Relational Analysis and K-NN Algorithm

Hande Hakan, Ecem Coşar Canlıer, Çiğdem Özarı, Esin Nesrin Can

2024, 36(1):  4-15. 

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The main purpose of this study is to forecast the countries’ socio-economic performance with the fewest possible parameters. To do this, we propose a model consisting of methods from Multi-Criteria Decision Making and Machine Learning. Since the existence of different classifications of countries and several socioeconomic parameters, it becomes difficult to make a prediction of their belonging group and compare countries based on these parameters. Using the Grey Relational Analysis and the Critic method, we classify the countries into four different subgroups based on several socio-economic dimensions. K-Nearest Neighbor (K-NN) algorithm with basic macro-economic parameters is implemented to predict the countries' socioeconomic groups. The results rank the countries according to their socio-economic performance and predict the countries’ development levels for the future. The main findings indicated that the proposed approach can be used for similar research questions. The highest prediction percentages are accurate for small values of k. This study provides a convenient and effective method for grouping countries at different levels of development using basic economic parameters and provides a simple and practical method to predict the belonging group.  

Supplier Risk Assessment Research Based on Improved QFD-GC Method with Choquet Integral

Daao Wang, Huan Wang, Zhigeng Fang

2024, 36(1):  16-21. 

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In the realm of production and manufacturing, a symbiotic relationship with suppliers underscores the significance of rigorous supplier risk assessment. To address this growing need, our approach comprises four essential stages. Firstly, we have pioneered the development of an interval grey number QFD platform, a pioneering tool designed to discern and prioritize pivotal quality risk factors. Secondly, the Choquet integral is skillfully employed to navigate the intricate web of risk events' interrelations, thereby deriving the essential weightings of these risk factors. Thirdly, a cutting-edge grey clustering evaluation model is meticulously crafted, integrating the weightings of the risk factors. This model, a cornerstone of our methodology, is instrumental in classifying suppliers based on their respective risk profiles, optimizing risk management strategies. Lastly, our method's practicality and effectiveness are unequivocally validated through a real-world numerical example, conclusively showcasing its value in the context of supplier risk management. 

Evaluation of Care Service Quality for Disabled Elderly Individuals in the Community Based on the Prospect-Grey Target House Model  

Yun Fan, Jun Liu, Shuli Yan, Na Zhang, Xiaojun Guo, Zhigeng Fang, Sifeng Liu

2024, 36(1):  22-31. 

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Considering the varying levels of disability among elderly people, the capability layer → demand layer → service layer structure was decomposed step by step. This enabled us to establish a quality house model that forges an association matrix between care needs and care service attributes for disabled elderly individuals residing in the community. Considering the decision maker's expected grey target and irrational risk attitude towards care service attributes, the prospect-grey target house care service quality evaluation model for disabled elderly individuals in the community was constructed based on prospect theory and grey target decision-making. By evaluating the quality of care services for disabled elderly individuals in the community, the care service levels of different types of disabled elderly individuals and groups that require improvements in care services were identified.  

On Grey Real Number and Its Operation Rules

Xican Li, Li Li

2024, 36(1):  32-44. 

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In order to reveal the mathematical mechanism of generating grey numbers and the law of grey number evolution, the extension principle of grey set is proposed in this paper firstly, which provides a theoretical basis for grey number operation. Secondly, based on the possibility function of grey set, the concept and properties of grey convex set are given. According to grey convex set, the definitions of grey real number, universal grey real number and interval grey number are put forward. Thirdly, the basic operation rules of grey real number are given based on the extension principle, and the operations of data block expression are further given to meet the reversibility of grey real number operation. Finally, the sufficient and necessary condition for the reversibility of universal grey real number operation is given, and it is proved that the grey real number operations using data block expression are reversible. Examples show that the grey real number operations using data block expression proposed in this paper are feasible and effective. The research results enrich the grey system theory and provide a theoretical basis for grey algebra research.  

A study on the grey relational weighted evaluation model for the selection of leading industries in the airport economic zone 

Hongqing Liao, Zhigeng Fang, Qin Zhang, Xiaqing Liu, Chuanhui Wang, Ding Chen, Xiaochao Qian

2024, 36(1):  45-55. 

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The evaluation of leading industries involves the use of evaluation index data that exhibit multi-source uncertainty. This implies that the evaluation index values encompass various types of numbers, such as grey numbers, white numbers, fuzzy numbers, interval value fuzzy numbers, and more. The evaluation index system possesses a multi-level structure with interconnections among the indicators. In this study, we propose a generalized grey relational weighted evaluation model based on multi-source uncertainty for assessing leading industries. To begin with, the generalized grey number is used to represent all uncertain data, and the weights of multi-level indicators are calculated by combining the generalized grey number with the information entropy model. Subsequently, the correlation between the indexes is examined utilizing the theorem of the generalized grey absolute relational degree model. This analysis leads to the construction of a generalized grey absolute relational degree matrix, from which eigenvalues and eigenvectors are derived. Based on the generalized grey weight of the multi-level indexes, the eigenvalue and eigenvector of the generalized grey absolute relational matrix, and the grey relational weighted evaluation model for leading industry evaluation are established. Finally, the effectiveness and feasibility of the proposed model are validated through a case study involving the evaluation of the leading industry in the airport economic zone.  

Interaction-based nonlinear INDGM(1,N) model and its application

Ye Li, Dongyu Liu, Junjuan Liu, Meidan Xiao

2024, 36(1):  56-62. 

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Multivariate grey models are commonly used to evaluate the independent effects of related factors, but they may fail to account for any nonlinear interactions that could exist between them. To address this limitation, this study introduces the INDGM(1,N) model, which considers the nonlinear interactions between related factors. Simultaneously, to depict the nonlinear impact of both the system behavior sequence and corresponding factor sequences more accurately, varying power parameters have been incorporated into the model proposed in this paper. Moreover, by adjusting the parameter values of the INDGM(1,N) model, it can be converted into several other models, such as the DGM(1,N) model, GM(1,N) model, DGM(1,1) model, or GM(1,1) model. This study uses a genetic algorithm to obtain the time response of the INDGM(1,N) model by solving its nonlinear characteristic parameters. We then use the model to simulate and forecast China's CO2 emissions and compare its performance with that of other models. The results show that the INDGM(1,N) model provides more accurate simulation and prediction accuracy than other models, highlighting its effectiveness. 

Time-Delay TLDBGM(1,N) model with dynamic background value and its application 

Dang Luo, Xinqing Qiao

2024, 36(1):  63-78. 

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Since the traditional multivariable grey prediction model has insufficient consideration of the coupling effect of background value and time-delay accumulative term, which leads to the low prediction accuracy of the model. Based on this, we propose a new multivariable time-delay grey prediction model with dynamic background value. The model adds dynamic background value coefficient, time-delay parameters, linear correction term, and grey action quantity term to the traditional GM(1,N) model. First, the delay periods of driver factors are determined by using the grey time-delay correlation analysis method. Second, the parameter estimation method of the model is discussed and the direct solution of the TLDBGM(1,N) time response function is given by defining the derived form of the TLDBGM(1,N) model. Finally, the model background value coefficient and time-delay parameters are identified and optimized based on the differential evolutionary algorithm. The model is applied to the problem of grain yield prediction in Henan Province. Result shows that the simulation and prediction accuracy of TLDBGM(1,N) are better than other multivariable grey prediction models. The model is theoretically more generalized. And it is shown that GM(1,1), GM(1,N), and TLGM(1,N) models are all special forms of the model for different parameter values.