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The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.

Grey modeling technique is an important element of grey system theory, and academic articles applied to agricultural science research have been published since 1985, proving the broad applicability and effectiveness of the technique from different aspects and providing a new means to solve agricultural science problems. The analysis of the connotation and trend of the application of grey modeling technique in agricultural science research contributes to the enrichment of grey technique and the development of agricultural science in multiple dimensions.

Based on the relevant literature selected from China National Knowledge Infrastructure, the Web of Science, SpiScholar and other databases in the past 37 years (1985–2021), this paper firstly applied the bibliometric method to quantitatively visualize and systematically analyze the trend of publication, productive author, productive institution, and highly cited literature. Then, the literature is combed by the application of different grey modeling techniques in agricultural science research, and the literature research progress is systematically analyzed.

The results show that grey model technology has broad prospects in the field of agricultural science research. Agricultural universities and research institutes are the main research forces in the application of grey model technology in agricultural science research, and have certain inheritance. The application of grey model technology in agricultural science research has wide applicability and precise practicability.

By analyzing and summarizing the application trend of grey model technology in agricultural science research, the research hotspot, research frontier and valuable research directions of grey model technology in agricultural science research can be more clearly grasped.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

Research on grey systems is becoming more sophisticated, and grey relational and prediction analyses are receiving close review worldwide. Particularly, the application of grey systems in marine economics is gaining importance. The purpose of this paper is to summarize and review literature on grey models, providing new directions in their application in the marine economy.

This paper organized seminal studies on grey systems published by Chinese core journal database – CNKI, Web of Science and Elsevier from 1982 to 2018. After searching the aforementioned database for the said duration, the authors used the CiteSpace visualization tools to analyze them.

The authors sorted the studies according to their countries/regions, institutions, keywords and categories using the CiteSpace tool; analyzed current research characteristics on grey models; and discussed their possible applications in marine businesses, economy, scientific research and education, marine environment and disasters. Finally, the authors pointed out the development trend of grey models.

Although researches are combining grey theory with fractals, neural networks, fuzzy theory and other methods, the applications, in terms of scope, have still not met the demand. With the increasingly in-depth research in marine economics and management, international marine economic research has entered a new period of development. Grey theory will certainly attract scholars’ attention, and its role in marine economy and management will gain considerable significance.

The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST).

GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper.

The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling.

Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect.

Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

In this study, a hybrid rough and grey set-based rule model is designed for diagnosis of one type of blood cancer called multiple myeloma (MM). The grey clustering method is used to combine the same condition attributes and to improve the validity of the final model.

Some tools of the rough set theory (RST) and grey incidence analysis (GIA) are used in this research to analyze the serum protein electrophoresis (SPE) test results. An RST-based rule model is extracted based on the laboratory SPE test results of patients. Also, one decision attribute and 15 condition attributes are used to extract the rules. About four rule models are constructed due to the different algorithms of data complement, discretization, reduction and rule generation. In the following phases, the condition attributes are clustered into seven clusters by using a grey clustering method, the value set of the decision attribute is decreased by using manual discretizing and the number of observations is increased in order to improve the accuracy of the model. Cross-validation is used for evaluation of the model results and finally, the best model is chosen with 5,216 rules and 98% accuracy.

In this paper, a new rule model with high accuracy is extracted based on the combination of the grey clustering method and RST modeling for diagnosis of the MM disease. Also, four primary rule models and four improved rule models have been extracted from different decision tables in order to define the result of SPE test of patients. The maximum average accuracy of improved models is equal to 95% and related to the gamma globulins percentage attribute/object-related reducts (GA/ORR) model.

The total number of observations for rule extraction is 115 and the results can be improved by further samples. To make the designed expert system handy in the laboratory, new computer software is under construction to import data automatically from the electrophoresis machine into the resultant rule model system.

The main originality of this paper is to use the RST and GST together to design and create a hybrid rule model to diagnose MM. Although many studies have been carried out on designing expert systems in medicine and cancer diagnosis, no studies have been found in designing systems to diagnose MM. On the other hand, using the grey clustering method for combining the condition attributes is a novel solution for improving the accuracy of the rule model.

The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity.

The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model.

The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations.

The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged.

The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.

Risk management is one of the most influential parts of project management that has a major impact on the success or failure of projects. Due to the increasing use of information technology in all fields and the high failure rate of software development projects, it is essential to predict the risk level of each project effectively before starting. Therefore, the main purpose of this paper is proposing an expert system to infer about the risk of new banking software development project.

In this research, the risk of software developing projects is considered from four dimensions including risk of cost deviation, time deviation, quality deviation and scope deviation, which is examined by rough set theory (RST). The most important variables affecting the cost, time, quality and scope of projects are identified as condition attributes and four initial decision systems are constructed. Grey system theory is used to cluster the condition attributes and after data discretizing, eight rule models for each dimension of risk as a decision attribute are extracted using RST. The most validated model for each decision attribute is selected as an inference engine of the expert system, and finally a simple user interface is designed in order to predict the risk level of any new project by inserting the data of project attributes

In this paper, a high accuracy expert system is designed based on the combination of the grey clustering method and rough set modeling to predict the risks of each project before starting. Cross-validation of different rule models shows that the best model for determining cost deviation is Manual/Jonson/ORR model, and the most validated models for predicting the risk of time, quality and scope of projects are Entropy/Genetic/ORR, Manual/Genetic/FOR and Entropy/Genetic/ORR models; all of which are more than 90% accurate

It is essential to gather data of previous cases to design a validated expert system. Since data documentation in the field of software development projects is not complete enough, grey set theory (GST) and RST are combined to improve the validity of the rule model. The proposed expert system can be used for risk assessment of new banking software projects

The risk assessment of software developing projects based on RST is a new approach in the field of risk management. Furthermore, using the grey clustering for combining the condition attributes is a novel solution for improving the accuracy of the rule models.