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At present, financial agglomeration tendency in domestic and foreign countries is increasingly evident. Therefore, from a comparative perspective, this paper aims to assess and predict the financial agglomeration degree in central five cities.

According to the diversity of evaluating indexes and the uncertainty of financial agglomeration, this paper constructs a set of indexes of evaluating the financial agglomeration degree, comprehensively evaluates the financial agglomeration degree of the five cities – Wuhan, Changsha, Zhengzhou, Nanchang and Hefei – in China's middle region from 2001 to 2010 by using the multiple dimension grey fuzzy decision-making model, and predicts their development tendency by using the GM (1, 1, β) model.

The results show that the multiple dimension grey fuzzy decision-making pattern cannot only be used to determine the weights of evaluating indexes, but also get the fuzzy partition and ranking order of the financial agglomeration in central five cities. The grey prediction results can objectively reflect the development tendency of the financial agglomeration in central five cities.

From the results, it is necessary for any competitive city to clarify their relative strengths and weaknesses in order for the accurate location and scientific development, and it also provides a reference for the government decision-making.

The paper succeeds in using the multiple dimension grey fuzzy decision-making model to measure the financial agglomeration degree of the five central cities and the grey prediction model to predict future trends.

As the grey systems theory has been used over the time in different economic areas, in the following, a short literature review will be put forward, starting from the usage of these theory in the supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, etc. The purpose of this paper is to identify some key studies from all the economic areas in which the grey systems can be used in order to open and to bring to the researchers new domains in which they can manifest their interest and in which they can successfully use the methods offered by the grey systems theory.

Using the search engine offered by the Web of Science, a literature review has been performed for the economic grey systems applications developed over the time on both economic diagnosis and system’s forecasting. In addition, some hybrid grey systems theory – artificial intelligence techniques models have also been presented.

The grey systems theory has brought its contribution to numerous economic application from various fields such as: supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, firms’ bankruptcy, product development, consumer income, monetization ratio, etc.

The present paper identifies the some of the most representative examples in which the grey theory has been used, but, in the same time, there are a lot of studies that have not been mentioned here due to the lack of space.

Unlike other review papers written on the grey systems theory area, the present paper is only focusing on the economic applications in which this theory has been successfully used, bringing to the reader a general overview on this field and, in the same time, enabling new research perspectives.

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.

By using small reference samples, the calculation method of confidence value and prediction method of confidence interval for multi-input system are investigated. The purpose of this paper is to offer effective assessing methods of confidence value and confidence interval for the simulation models used in establishing guidance and control systems.

In this paper, first, an improved cluster estimation method is proposed to guide the selection of the small reference samples. Then, based on analytic hierarchy process method, the new calculation method of the weight of each reference sample is derived. By using the grey relation analysis method, new calculation methods of the correlation coefficient and confidence value are presented. Moreover, the confidence interval of the sample awaiting assessment is defined. A new prediction method is derived to obtain the confidence interval of the sample awaiting assessment which has no reference sample. Subsequently, by using the prediction method and original small reference samples, Bootstrap resampling method is used to obtain more correlation coefficients for the sample to reduce the probability of abandoning the true.

The grey relational analysis is used in assessing the confidence value and interval prediction. The numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Based on the selected small reference samples, new calculation methods of the correlation coefficient and confidence value are presented to assess the confidence value of model awaiting assessment. The calculation methods of maximum confidence interval, expected confidence interval and other required confidence intervals are presented, which can be used in assessing the validities of controller and guidance system obtained from the model awaiting assessment.

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.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

The purpose of this study is to make a prediction of China's energy consumption structure from the perspective of compositional data and construct a novel grey model for forecasting compositional data.

Due to the existing grey prediction model based on compositional data cannot effectively excavate the evolution law of correlation dimension sequence of compositional data. Thus, the adaptive discrete grey prediction model with innovation term based on compositional data is proposed to forecast the integral structure of China's energy consumption. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of China's energy consumption structure is conducted into a future horizon from 2021 to 2035 by using the model.

China's energy structure will change significantly in the medium and long term and China's energy consumption structure can reach the long-term goal. Besides, the proposed model can better mine and predict the development trend of single time series after the transformation of compositional data.

The paper considers the dynamic change of grey action quantity, the characteristics of compositional data and the impact of new information about the system itself on the current system development trend and proposes a novel adaptive discrete grey prediction model with innovation term based on compositional data, which fills the gap in previous studies.

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.

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.