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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.

On the basis of the given absolute incidence degree, a new absolute incidence degree is defined. It not only possesses the characteristic of invariant translational transformation, but also can describe the incidence property between every two sequences exactly.

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 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.

As an important measure to promote sustainable development, green finance has developed rapidly in recent years. In order to comprehensively analyze the positive and negative indicators of the influencing factors of green finance, this paper puts forward a grey relational method of spatial-temporal panel data from the perspective of the development trend of the object dimension indicators and the performance difference between the time dimension indicators.

From the different perspectives of object dimension and time dimension, the positive and negative indicators are standardized differently considering the reverse of indicators and characterizing factors. The grey absolute relational degree is used to define the matrix sequence. This method reflects the development trend of objects in time and the difference characteristics among objects, which comprehensively represents the correlation between the reference panel and the comparison panel.

The results show that: (1) The object dimension reflects the internal driving force of the development of green finance in each provincial administrative region and the time dimension reflects the relationship between regional differences of influencing factors and green finance. (2) From the object dimension, the influencing factors of green finance from high to low are economic development potential, economic development level, air temperature, policy support, green innovation and air quality. (3) From the time dimension, the influencing factors of green finance from high to low are green innovation, air quality, economic development potential, economic development level, policy support and air temperature.

The different standardized processing methods of positive and negative indicators proposed in this paper not only eliminate the sample dimension, but also study the grey relational degree among the indicator panels from different reference dimensions. The proposed model is applied to identify the influencing factors of green finance, which expands the practical application scope of the grey relational model. The research results can provide reference for relevant departments to better promote the development of green finance.

The purpose of this paper is to study the properties of comprehensive incidence degrees of closeness incidence degrees and similitude incidence degrees.

Based on the new definitions of the closeness incidence degree and the similitude incidence degree, the properties of comprehensive incidence of closeness incidence and similitude incidence are studied in this paper. It is proved that weighted arithmetic average of two closeness incidence degrees as well as power product (including weighted geometric average) of two closeness incidence degrees is still closeness incidence degree; and arithmetic weighted average of two similitude incidence degrees as well as power product (including weighted geometric average) of two similitude incidence degrees is still similitude incidence degree. Mixed weighted arithmetic average of closeness incidence degree and similitude incidence degree and mixed power product (including weighted geometric average) of closeness incidence degree and similitude incidence degree are closeness incidence degrees.

The result shows that the effect of closeness incidence degree is stronger than similitude incidence degree. As long as the weight of closeness incidence degree is not equal to zero, the comprehensive incidence degree results are closeness incidence degrees.

Grey incidence degrees have been widely applied in many fields, such as the test of grey model's forecasting effect, the system analysis and so on. The obtained result in this paper is to illustrate two kinds of incidence degrees are incompatible, namely there does not exist both closeness and similitude incidence degree.

The paper succeeds in showing that the attempt to get comprehensive incidence degree by arithmetic or geometric weighted average of closeness incidence degree and similitude incidence degree to reflect both closeness and similarity is in vain. And it is undoubtedly a new development in grey system theory.

The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.

The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.

It will promote the accuracy of multivariate grey incidence model.

The purpose of this paper is to present the terms of grey incidence analysis models.

The definitions of basic terms about various grey incidence analysis models are presented one by one.

The reader could know the basic explanation about the important terms about various grey incidence analysis models from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

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.

This study aims to investigate how and to what extent structural network properties affect dyadic negotiation behavior in tourism destination ecosystems. Specifically, this study addresses negotiation behavior in terms of problem-solving and contending, because these two key strategies reflect the integrative and distributive aspects of dyadic interactions.

This study relies on network data and dyadic survey data from nine mountain tourism destinations in Southeastern Norway. The structural network properties the authors research are triadic closure – the extent to which a dyad has common ties to other actors – and structural equivalence – the similarities in networking patterns that capture firms’ competition for similar resources. In addition, the authors also study a possible effect of relationship duration on negotiation behavior.

Triadic closure and relationship duration have positive effects on problem-solving, and structural equivalence tends to decrease problem-solving, although the effect is inconsistent; none of these three independent variables was found to affect contending negotiation behavior.

This study shows that a dyad’s structural network embeddedness has implications for negotiation behavior. Further research is encouraged to develop this theoretical perspective.

This study is a pioneering investigation of how structural network properties affect dyadic negotiation behavior in ongoing coproducing relationships in real-world destination ecosystems.