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The purpose of this paper is to evaluate resource configuration and service ability in hospital on public private partnership (PPP) model (Chaonan Minsheng Hospital of Guangdong Province), supplying decision-making reference for participants of hospital on PPP model.

Four model of grey relational analysis (GRA) (Deng's correlation degree, grey absolute correlation degree, grey relative correlation degree and grey comprehensive correlation degree) are applied to evaluate resource configuration and service ability, a total of 11 indicators of hospital on PPP model public hospital and private hospital from 2007 to 2011.

The paper finds that different GRA models have different results when the paper applied them to evaluate resource configuration and service ability in hospital on PPP model. More than 60 per cent indicators of resource configuration (total six indicators) and service ability (total six indicators) are assessed as “hospital on PPP model ≻ public hospital” or “hospital on PPP model≻ private hospital” from three models of Deng's correlation degree, grey absolute correlation degree and grey comprehensive correlation degree.

Evaluation of resource configuration and service ability for hospital on PPP model with GRA makes results quantified objective and provides reference for decision making and management. GRA makes the comparison of resource configuration and service ability between hospital on PPP model and other model hospitals becoming possible.

The shortcoming for data analysis method of “large sample” is overcome and data analysis method of “small sample” is realized by using GRA, which broaden the method of evaluating hospital on PPP model.

The purpose of this paper is to find the key influence factors of executive compensation within China ports and listed shipping companies and provide some reasonable suggestions. Eventually, help to perfect the executive compensation evaluation mechanism against the background of new area.

Grey correlation analysis is an important part of grey system theory. Professor Liu Sifeng further studies the relationship between two sequences absolute increment on the basis of Deng’s degree and put forward the “Grey absolute correlation degree,” which is widely used in practice. In the study, on the basis of the area of the line between sequences size, it measures the correlation degrees of firm performance, executive stock holding, continuous growth capacity and other relevant factors of executive payment in China ports and listed shipping companies.

The paper concludes that the main factors influence CEO salary in China ports and listed shipping companies are return on equity and growth rate of fixed assets. However, the authors consider the frequent occurrence of executives’ corruption in China listed state-owned enterprise under the environment of financial and economic crisis, the authors argue that the significant influence of net assets attributed to shareholders cannot be ignored. In addition, cash flow in operating activities and executive stock holding both have relatively important effect on executive compensation.

This paper still has some limitations. First, it merely takes into account the financial indicators and ignores the influence of non-financial indicators to the performance evaluation of listed companies, such as: innovation ability, human capital and goodwill. Second, it has not considered the power consumption and other types of “invisible income” in the executive compensation structure, neither the influence of investing and financing activities on corporate performance. Consequently, these are likely to cause a certain deviation to the results of the study.

The outcome obtained in this paper can be provided for China ports and listed shipping companies to establish a reasonable executive compensation evaluation and incentive mechanism under the background of depressed shipping market.

This paper intends to use correlation analysis between firm performance, executive stock holding, sustainability and executive compensation in the new area of time, tries to make a greater contribution to the major component of salary policy and then make some suggestions on incentive supervising and restraining mechanisms for the ports and listed shipping firms in China.

Although scholars have done many studies about the association analysis of executive compensation and firm performance, they neglect the economic environment of industry. Meanwhile, considering the non-financial indicators and incomplete information, this paper studies the grey correlation analysis of executive compensation and influence factors in China ports and listed shipping firms under the background of the Chinese flagging shipping industry.

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 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.

This paper attempts to extend classic absolute degree of grey incidence so that the extended model can be used for grey number sequences.

The classic absolute degree of grey incidence was extended according to basic principles of grey incidence analysis. First, modelling methods and theories of the classic grey incidences were summarized. Then, the zeroing starting operator in grey incidence was extended for grey sequence. Third, the parameters in classic incidence degree were redefined, and an absolute degree of grey incidence for grey number sequences was proposed. The degree can not only be applied to grey number sequence, but also contains the uncertain information of analysis result. Fourth, two non‐linear programming models were constructed to estimate the grey coverage interval of absolute degree of incidences. Finally, the comparison method of grey numbers was introduced for sorting the different absolute degrees of incidences.

A theoretically feasible absolute degree of grey incidence was constructed for grey sequence. A case study showed that the proposed incidence degree was an effective method for grey sequence incidence analysis.

The method exposed in the paper can be used for grey sequences clustering, grey decision making, multi‐attribute decision making theory, uncertain target recognition and other related fields.

The paper succeeded in establishing an incidence analysis model for grey sequences which was still a research gap in grey system theory.

The purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences.

The definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied.

The negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility.

The proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model.

The definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

The purpose of this paper is to construct a grey clustering model based on the nonlinear whitenization weight function and to assess the safety of civil aircraft by using a quantitative method.

According to the running stage of civil aircraft safety assessment issues, first the civil aircraft safety evaluation index system is constructed by using a qualitative method. Taking the information duplication between indicators, the grey relational analysis method is used to filter the key indicators, then the grey clustering evaluation model of nonlinear whitening right function is built to evaluate the safety of civil aircraft and the algorithm steps of the evaluation model are given. Finally, the model is validated by collecting the parameters of nine different civil aircrafts at home and abroad.

The results show that the safety level of different types of aircraft is different due to the different index parameters, and to some extent, explain the rationality and scientificity of the method proposed in this paper to solve the problem.

This paper gives a complete set of security assessment methods, which can be used to evaluate the security of civil aircraft in the operational phase quantitatively, scientifically and reasonably. Furthermore, it can be extended to other complex system security or stability assessment issues.

It not only provides the supplement and perfection of the safety assessment method in the theoretical system to a certain extent, but also provides a theoretical guidance to solve the problem of civil aircraft system safety assessment of civil aircraft manufacturing enterprise all over the world. At the same time, the nonlinear grey clustering evaluation model constructed in this paper is an improvement of the traditional model, which is, to some extent, the improvement of the grey clustering evaluation theory.

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 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.

Equally weighted factors and initial data from behavioural sequences are used for calculating the degree of grey incidence in Deng’s grey incidence analysis. However, certain grey information cannot be directly obtained, and the correlation coefficients of each sequence at different times are of different importance to the system. The purpose of this paper is to propose an improved grey incidence model with new grey incidence coefficients and weighted degree of grey incidence. Some grey information can be obtained more easily by using the grey transformation sequences, and the maximum entropy method is used to calculate the weights of new grey incidence coefficients, so the new degree of grey incidence was distinguished more effectively by the proposed model.

New grey incidence coefficients are defined using transformation sequences of the initial data. To overcome the shortcomings arising from the use of equal weights, the maximum entropy method is proposed for determining the weights of the grey incidence coefficients. The resulting model optimises the classical models and evaluates the influencing factors more effectively. The effectiveness of the model was verified by a numerical example. Furthermore, the model was used for analysing the main influencing factors of the tertiary industry in China.

The proposed model optimises the classical models, and the application example shows that urbanisation has the greatest effect on employment in the tertiary sector.

An improved grey incidence model is proposed that improves the grey incidence coefficients and their weights, and has better performance than the classical models. The model was successfully used in the analysis of the influence factors of the tertiary industry in China. The results indicate that the model can reflect the significance of incidence coefficients at different time points; therefore, their fluctuation can be effectively controlled.