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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 purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.

This paper aims to deal with the grey relational problem of panel data with an attribute value of interval numbers. The grey relational model of interval number for panel data is constructed in this paper.

First, three kinds of interval grey relational operators for the behavior sequence of a dimensionless system are proposed. At the same time, the positive treatment method of interval numbers for cost-type and moderate-type indicators is put forward. On this basis, the correlation between the three-dimensional interval numbers of panel data is converted into the correlation between the two-dimensional interval numbers in time series and cross-sectional dimensions. The grey correlation coefficients of each scheme and the ideal scheme matrix are calculated in the two dimensions, respectively. Finally, the correlation degree of panel interval number and scheme ordering are obtained by arithmetic mean.

This paper proves that the grey relational model of the panel interval number still has the properties of normalization, uniqueness and proximity. It also avoids the problem that the results are not unique due to the different orders of objects in the panel data.

The effectiveness and practicability of the model is verified by taking supplier selection as an example. In fact, this model can also be widely used in agriculture, industry, society and other fields.

The accuracy of the relational results is higher and more accurate compared with the previous studies.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

The purpose of this paper is to study the essential characteristics of grey relational degree of proximity, to analyse the abstract meaning of grey relational degree of similarity and fully consider the two different relational degree models.

The paper constructed the grey proximity relational degree by using the weighted mean distance. To analyse the motivation of the development of things, this paper constructed the grey similarity degree by using the concept of induced strength. Finally, the two correlation models are weighted by reliability weighting.

The research finding shows that the distance is the essence of the grey relational degree of proximity, and the induced strength is a good explanation of the similarities in the development of things.

The analyses imply that the total amount of water consumption in China has the greatest correlation with the consumption of agricultural water resources, followed by the consumption of industrial water resources, and the least correlation with the consumption of domestic water resources.

The paper succeeds in realizing the essential characteristics of grey relational degree of proximity and the abstract meaning of grey relational degree of similarity. Besides, the resolution of the correlation degree can be greatly improved by reliability weighting.

Since 2000, China, along with the USA, UK, France, Japan and many other developed countries have drawn up new blueprints for the development of a marine economy. At present, international marine economics research has entered into a new period of development, and the research methods of ocean econometrics are becoming more complex and mature. The purpose of this paper is to review the progress of international marine econometrics research and gives the development direction of marine econometrics.

The Web of Science core collection database was utilized, harvesting data from 1996 to May 2018, measuring the marine economy research from 1,489 articles as its sample, using CiteSpace visualization analysis tools.

Mapping the knowledge map from annual international marine economic metrology, literature identification, keywords, involving disciplines and related journals, countries (regions) and research and analyzing the research status of reveals the research frontiers of international marine economy measurement (learning) by using CiteSpace.

The conceptions and characteristics of marine econometrics are defined and analyzed, and the theoretical method of marine econometrics is sorted out. Mapping the knowledge diagram of marine econometrics and discussing the research status of international marine economics, and clarifying the existing problems, future opportunities and challenges of international marine econometrics research.

The purpose of this paper is to measure the high-quality development level of China's marine economy and analyze corresponding spatial and temporal distribution characteristic.

Design and optimize the index system of high-quality development level of marine economy and use entropy and TOPSIS method for comprehensive evaluation.

The research finds that from 2017 to 2019, the high-quality development tendency of China's marine economy is on the rise, but the overall level is still low. The level of each subsystem has different distribution characteristics in different provinces and cities. Guangdong, Shandong and Shanghai have a high comprehensive level. According to the comprehensive level of high-quality development of marine economy, 11 coastal provinces are divided into three types: leading, general and backward.

This paper clarifies the temporal and spatial distribution law of high-quality development level of China's marine economy, providing basis for promoting comprehensive and coordinated improvement of coastal provinces and cities.

An indicator system for the high-quality development level of the marine economy has been established, including social development guarantee, marine economic foundation, marine science and technology drive and green marine sustainability.

On the basis of the time series of the land area economy and marine economy data during 1996-2015, the authors study the relationship between land area economy and marine economy, and divides the relational schema of the land-sea economy by doing causality test of land-sea economy, grey correlation degree analysis and relational schema analysis of the land-sea economy in coastal provinces and cities. The paper aims to discuss these issues.

The paper uses methods such as Granger causality test and grey correlation degree analysis to preliminarily demonstrate the relationship of land-sea economy.

With Granger causality test, we can draw that there is a causal relationship between the land area economy and marine economy. Further with the relational schema analysis, we can draw that the relationship between marine economy and land economy in 11 coastal provinces and cities can be summed up into four kinds of patterns such as land-sea weak type, land-sea strong type, sea strong land weak type and land strong sea weak type.

For the government and related disaster management departments, when policies are made and relevant measures are taken in the process of planning economic layout of land-sea economy, similar policies or measures may be taken for the same type of provinces, in order to improve administrative efficiency.

The development and utilization between land economy and marine economy has a certain contradiction, which must be balanced to realize the balanced development of land economy and marine economy. Therefore, it is necessary to comprehensively assess the grey relational analysis of land-sea economy, in order to provide the basis for reasonable policies.

To construct a scientific and reasonable indicator system, it is necessary to design a set of standardized indicator primary selection and optimization inspection process. The purpose of this paper is to provide theoretical guidance and reference standards for the indicator system design process, laying a solid foundation for the application of the indicator system, by systematically exploring the expert evaluation method to optimize the index system to enhance its credibility and reliability, to improve its resolution and accuracy and reduce its objectivity and randomness.

The paper is based on system theory and statistics, and it designs the main line of “relevant theoretical analysis – identification of indicators – expert assignment and quality inspection” to achieve the design and optimization of the indicator system. First, the theoretical basis analysis, relevant factor analysis and physical process description are used to clarify the comprehensive evaluation problem and the correlation mechanism. Second, the system structure analysis, hierarchical decomposition and indicator set identification are used to complete the initial establishment of the indicator system. Third, based on expert assignment method, such as Delphi assignments, statistical analysis, t-test and non-parametric test are used to complete the expert assignment quality diagnosis of a single index, the reliability and validity test is used to perform single-index assignment correction and consistency test is used for KENDALL coordination coefficient and F-test multi-indicator expert assignment quality diagnosis.

Compared with the traditional index system construction method, the optimization process used in the study standardizes the process of index establishment, reduces subjectivity and randomness, and enhances objectivity and scientificity.

The innovation point and value of the paper are embodied in three aspects. First, the system design process of the combined indicator system, the multi-dimensional index screening and system optimization are carried out to ensure that the index system is scientific, reasonable and comprehensive. Second, the experts’ background is comprehensively evaluated. The objectivity and reliability of experts’ assignment are analyzed and improved on the basis of traditional methods. Third, aim at the quality of expert assignment, conduct t-test, non-parametric test of single index, and multi-optimal test of coordination and importance of multiple indicators, enhance experts the practicality of assignment and ensures the quality of expert assignment.

The purpose of this paper is to examine the effectiveness of an improved dummy variables control grey model (DVCGM) considering the hysteresis effect of government policies in China's energy intensity (EI) forecasting.

Energy consumption is considered as an important driver of economic development. China has introduced policies those aim at the optimization of energy structure and EI. In this study, EI is forecasted by an improved DVCGM, considering the hysteresis effect of energy-saving policies of the government. A nonlinear optimization method based on particle swarm optimization (PSO) algorithm is constructed to calculate the hysteresis parameter. A one-step rolling mechanism is applied to provide input data of the prediction model. Grey model (GM) (1, N), DVCGM (1, N) and ARIMA model are applied to test the accuracy of the improved DVCGM (1, N) model prediction.

The results show that the improved DVCGM provides reliable results and works well in simulation and predictions using multivariable data in small sample size and time-lag virtual variable. Accordingly, the improved DVCGM notes the hysteresis effect of government policies and significantly improves the prediction accuracy of China's EI than the other three models.

This study estimates the EI considering the hysteresis effect of energy-saving policies in China by using an improved DVCGM. The main contribution of this paper is to propose a model to estimate EI, considering the hysteresis effect of energy-saving policies and improve forecasting accuracy.