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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.

The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.

Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.

The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.

The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.

The purpose of this paper is to put forward the grey relational decision-making model of three-parameter interval grey number based on Analytic Hierarchy Process (AHP) and Data Envelopment Analysis (DEA), based on the previous study of grey relational decision-making model, and it considers the advantages of the decision-making schemes and the subjective preferences of decision makers.

First of all, through AHP, the preference of each index is analyzed and the index weight is determined. Second, the DEA model is adopted to obtain the index weight from the perspective of the most beneficial to each scheme and objectively reflect the advantages of different schemes. Then, assign the comprehensive weights to each index of the grey relational decision-making model of three-parameter interval grey number, and calculate the grey relation degree of each scheme to rank the schemes.

The effectiveness of the model is proved by an example of carrier aircraft selection.

The applicability of this model is analyzed by taking carrier aircraft selection as an example. In fact, this model can also be widely used in agriculture, industry, economy, society and other fields.

In this paper, the combination of AHP and DEA is used to determine the index weight. Based on which, the grey relation degree under the three-parameter interval grey number is calculated. It intended the application space of the grey relational decision-making model.

Although the applications of grey system theory have been prosperous in the engineering field, there are very few applications to the management field. We argue that this theory is worthy of promotion to the management field. Therefore, the main purpose of this study is to demonstrate the application of grey relation analysis, one part of the grey system theory, by analyzing the topic of service quality and customer satisfaction. Customers of the auto repair industry were chosen to find out the grey relation order of Parasuraman et al.’s ten factors. Tries to prove whether or not service quality and customer satisfaction are two different constructs. Finally, tries to verify the relative importance of technical quality and functional quality on service quality and customer satisfaction. The following is an enumeration of the important conclusions: each quality factor has a different effect upon service quality; each quality factor has a different effect upon customer satisfaction; service quality and customer satisfaction are different constructs in the minds of the consumers; technical quality and functional quality are of equal importance to service quality and customer satisfaction.

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 establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.

The classification of aircraft failures has been a significant part of functional hazard analysis (FHA). Aiming at the shortcomings of the traditional FHA method in the evaluation of aircraft risk, the purpose of this paper is to put forward a new approach by combining the gray comprehensive relation calculation method in the gray system theory with the traditional FHA in order to deal with the problem of “little data, poor information.”

This paper combines FHA, 1–9-scale method and gray relation analysis. At first, aircraft failure scenarios are chosen and data from experts are collected; then gray system theory is applied to find the relevance of such scenarios. Finally, the classification according to relevance is determined.

In the past, “little data, poor information” made it difficult for researchers to implement FHA. In this paper, the authors manage to deal with the problem of “poor information” and provide an approach to find the seriousness of aircraft failure.

Due to the use of expert-evaluating methods, the classification of failures is still a little subjective and can be improved in this area. In the future, the method can be improved from the perspective of combining FMEA to analyze more complex indicators or using multisource heterogeneous solutions to solve fuzzy numbers, probabilities, gray numbers and indicators that cannot be assigned.

The paper uses FHA to divide the failure state and establishes a gray evaluation model of the aircraft failure state classification to verify the relevant method. Some aircraft safety design requirements are used to check the safety hazards of the aircraft during the design process, and to provide rational recommendations for the functional design of the aircraft.

Improving the safety of aircraft is undoubtedly of great practical significance and has become a top priority in the development of the civil aviation industry. In this paper, the FHA method and the failure state of the aircraft are studied. The original FHA method is innovated by using the gray system theory applicable to the poor information state. Therefore, to some extent, this study has significance for improving the safety of civil aircraft flight, ensuring people’s travel safety and enhancing the society’s trust in civil aviation.

The main innovation of this paper is integrating the FHA method and the gray system theory. This study calculates the comprehensive relation degree of each failure under different flight stages, and uses FHA to divide the failure state, and finally establishes a gray evaluation model of the aircraft failure state classification to analyze the different conditions of the landing gear brake system, so that it improves the present situation, and the problem with the character of “little data, poor information” can be addressed better.

The purpose of this paper is to analyse the relationship between outpatient satisfaction and the five constructs of healthcare projects’ service quality in Pakistan using Deng’s grey incidence analysis (GIA) model, absolute degree GIA model (ADGIA), a novel second synthetic degree GIA (SSDGIA) model and two approaches of decision-making under uncertainty.

The study proposes a new synthetic GIA model and demonstrates its feasibility on data (N=221) collected from both public and private sector healthcare projects of Punjab, the most populous province of Pakistan, using a self-administered questionnaire developed using the original SERVQUAL approach.

The results of decision analysis approach indicated that outpatients’ satisfaction from the private sector healthcare projects is higher as compared to the public healthcare projects’. The results from the proposed model revealed that tangibility and reliability play an important role in shaping the patient satisfaction in the public and private sectors, respectively.

The study is pioneer in evaluating a healthcare system’s service quality using grey system theory. The study proposes the SSDGIA model as a novel method to evaluate parameters comprehensively based on their mutual association (given by absolute degree of grey incidence) and inter-dependencies (given by Deng’s degree of grey incidence), and tests the new model in the given scenario. The study is novel in terms of its analysis of data and modelling. The study also proposes a comprehensive structure of the healthcare delivery system of Pakistan.

The purpose of this study to provide a reference basis for effectively managing the risk of agrometeorological disasters in Henan Province, speeding up the establishment of a scientific and reasonable system of agrometeorological disasters prevention and reduction and guaranteeing grain security.

Firstly, according to the statistical data of areas covered by natural disaster, areas affected by natural disaster, sown area of grain crops and output of grain crops from 1979 to 2018 in Henan Province, China. We have constructed an agrometeorological disaster risk assessment system for Henan province, China, which is composed of indicators such as rate covered by natural disaster, rate affected by natural disaster, disaster coefficient of variation and disaster vulnerability. The variation characteristics of agrometeorological disasters in Henan Province and their effects on agricultural production are analyzed. Secondly, the grey relational analysis method is used to analyze the relation degree between the main agrometeorological disaster factors and the output of grain crops of Henan Province. Based on the grey BP neural network, the rate covered by various natural disaster and the rate affected by various natural disaster are simulated and predicted.

The results show that: (1) the freeze injury in the study period has a greater contingency, the intensity of the disaster is also greater, followed by floods. Droughts, windstorm and hail are Henan Province normal disasters. (2) According to the degree of disaster vulnerability, the ability to resist agricultural disasters in Henan Province is weak. (3) During the study period, drought and flood are the key agrometeorological disasters affecting the grain output of Henan Province, China.

The systematic analysis and evaluation of agrometeorological disasters are conducive to the sustainable development of agriculture, and at the same time, it can provide appropriate and effective measures for the assessment and reduction of economic losses and risks.

By calculating and analyzing the rate covered by natural disaster, the rate affected by natural disaster, disaster coefficient of variation and disaster vulnerability of crops in Henan Province of China and using grey BP neural network simulation projections for the rate covered by various natural disaster and the rate affected by various natural disaster, the risk assessment system of agrometeorological disasters in Henan is constructed, which provides a scientific basis for systematic analysis and evaluation of agrometeorological disasters.

The purpose of this study is to construct a gray relational model based on information diffusion to avoid rank reversal when the available decision information is insufficient, or the decision objects vary.

Considering that the sample dependence of the ideal sequence selection in gray relational decision-making is based on case sampling, which causes the phenomenon of rank reversal, this study designs an ideal point diffusion method based on the development trend and distribution skewness of the sample information. In this method, a gray relational model for sample classification is constructed using a virtual-ideal sequence. Subsequently, an optimization model is established to obtain the criteria weights and classification radius values that minimize the deviation between the comprehensive relational degree of the classification object and the critical value.

The rank-reversal problem in gray relational models could drive decision-makers away from using this method. The results of this study demonstrate that the proposed gray relational model based on information diffusion and virtual-ideal sequencing can effectively avoid rank reversal. The method is applied to classify 31 brownfield redevelopment projects based on available interval gray information. The case analysis verifies the rationality and feasibility of the model.

This study proposes a robust method for ideal point choice when the decision information is limited or dynamic. This method can reduce the influence of ideal sequence changes in gray relational models on decision-making results considerably better than other approaches.