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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 identify most favorable (or quasi-preferred) industry characteristics of remanufacturing industry and most favorable (or quasi-preferred) industry factors which have an effect on these characteristics so as to improve these factors.

Grey system theory has prominent advantage of using few data and uncertainty information to analyze many factors. Therefore, it is more suited for system analysis than traditional statistical analysis methods like regression analysis, variance analysis and principal component analysis, which require massive data, certain probability distribution in the data and few variant factors. So in this paper, grey incidence analysis method, which is an important part of grey system theory, is used to identify industry characteristics and key industry factor of remanufacturing industry in China and then put forward appropriate industrial policies and countermeasures to improve these industry factors.

According to the results of this study, it reveals that there are no most favorable industry characteristics and no most favorable industry factors in remanufacturing industry of China. “Annual sale of remanufacturing industry” is identified as quasi-preferred industry characteristic, and “total number of employees with master degree or above in remanufacturing enterprise” is identified as the quasi-preferred industry factor. “Total building area of remanufacturing enterprise” is referred as the most unfavorable industry factors.

Judging from the findings of this study, four practical implications are summarized as follows: “annual sale of remanufacturing industry” should be given great importance because it is a quasi-preferred industry characteristic. “Total number of employees with master degree or above in remanufacturing enterprise” and “total number of research institution and university participated in remanufacturing” should be further strengthened by establishing an industry-university-research institute collaboration network, due to the fact that they are the top two quasi-preferred industry factors. “Total investment of remanufacturing industry” and “total annual R&D expenditures” have not played their due role in improving remanufacturing industry, so they should be moderately controlled so as to reduce waste of investment. “Total building area of remanufacturing enterprise” must be strictly controlled because of its little impact on remanufacturing industry.

In this research, grey incidence analysis is applied to identify key industry factors of remanufacturing industry for the first time. It helps in finding industry factors which are in urgent need of improvement and assists in making appropriate industrial policies and countermeasures to improve them by studying relationships between industry characteristic and industry factors.

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.

The purpose of this paper is to construct a novel delay grey incidence analysis model to analyze drivers and obstacles of university R&D performance.

With respect to the fact that university R&D activities typically experience two stages of knowledge creation and technology transfer, and different drivers and obstacles come into play to affect the conversion of R&D investment to outcomes at each stage, based on the thought of grey incidence analysis and the specific characteristics of science and technology (sci-tech) development, a novel delay grey incidence analysis model is proposed in this paper, and then according to the yearbook statistical data, Chinese university R&D activities are investigated and the drivers and obstacles of university R&D performance are analyzed.

The results show that the R&D full-time staff and R&D funds of basic research are the key drivers of influencing factors, and the sci-tech innovation talents in universities’ R&D institutions and experiment development funds are the restraining factors to improve R&D performance in the stage of knowledge creation; the expenses of R&D achievement application and technology service and the full-time staff of achievement application and technology service are the key drivers and obstacles of influencing the aggregate amount of patent sale respectively.

This research helps policy makers to reflect on their university R&D policies and understand how to enhance the technology transfer rate in China.

The paper succeeds in identifying key drivers and obstacles of affecting university R&D performance in China by examining the input and output incidence at both the knowledge creation and technology transfer stages.

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 purpose of this paper is to evaluate and rank the influence of internet public opinion of China’s Government work in 2015 by weighted absolute degree of grey incidence with TOPSIS.

This disaggregation method includes four main steps, determine the vector of weights for the factors by analytic hierarchy process, calculate the matrix of consistent effect measure, determine the weighted absolute degree of grey incidence with TOPSIS, rank and evaluate the events.

We get the ranking of internet public opinion of China’s Government work in 2015 by weighted absolute degree of grey incidence with TOPSIS. The result can be used for evaluating and ranking the influence of internet public opinion in China. The positive weighted absolute degree of grey incidence, the negative weighted absolute degree of grey incidence and the weighted absolute degree of grey incidence with TOPSIS have the same ranking results. The same ranking results show that the method of weighted absolute degree of grey incidence with TOPSIS has good consistency.

The weighted absolute degree of grey incidence with TOPSIS can be easily used for other evaluation.

The weighted absolute degree of grey incidence with TOPSIS is proposed and first used for evaluating and ranking the influence of internet public opinion of China’s Government work.

The aggregation of information from a group of decision experts for developing collective opinion is the important question in practice. The purpose of this paper is to provide a group decision-making method via ordered weighted aggregation (OWA) operator and grey incidence analysis.

In this study, OWA operator provides aggregation of attribute values to form an overall decision for each decision expert, and grey incidence model provides aggregation of decision experts’ evaluations to form overall score for each alternative. The example illustrates the procedure and practicability of the proposed model.

A new thought for multiple attribute group decision-making problems is given. The proposed method produces an overall desirability score for each alternative.

This is to obtain a more comprehensive and realistic solution to the given group decision-making problem. The proposed analysis method of group decision-making problems reveals vitality of grey systems theory.

This paper combines OWA operator and grey incidence analysis to obtain a novel and effective method for group decision making. It is suitable for group decision-making problems in which the attribute weights are completely unknown, expert weights are completely unknown.

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 paper attempts to design an efficient algorithm for bearing track correlation of multi‐sensor on the same platform using grey incidence analysis which is on the basis of the line segment Hausdorff distance.

Starting from the line segment, Hausdorff distance that has been extended to calculate the distance between line segment sets by many scholars has been used for face recognition achieving good results. The degree of grey incidence is defined based on the above distance and properties which include normality, symmetry and closeness, are proved. Furthermore, a grey incidence matrix is built. With only the azimuth information detected by bearing sensors track correlation is difficult to judge, however grey incidence analysis can quickly and accurately determine whether two tracks are from the same target, and so an algorithm is designed to solve this dilemma. In the last part of the paper simulation experiment is conducted.

The results are convincing: not only the algorithm proposed in the paper can solve the problem of track correlation of bearing‐only sensors, but also the algorithm can judge the correlation degree of both tracks even in the case of intensive targets.

The method exposed in the paper can be used to judge correlation degree of tracks detected by different sensors even for less information, and also be used to determine the similarity of two waveforms in the field of engineering.

The paper succeeds in introducing the line segment Hausdorff distance into grey incidence analysis and on the basis of that an algorithm is designed to solve the problem of track correlation.

This paper attempts to analysis the credit risk at the angle of industrial and macroeconomic factor using grey incidence analysis method.

Credit asset quality problem is one of the obstacles limiting the further development of commercial banks; the research on credit risk becomes an important part of the implementation of a commercial bank's risk management. Different industries may have different effects on the credit risk of commercial bank. This paper proposes finding out the different incidences between industries and credit risk, as well as macroeconomics. Incidence identification method is established to investigate whether the industry and macroeconomic factor could affect an impaired loan ratio of a bank using the grey incidence analysis method.

The results indicate that the impaired loan ratio differs with diverse industry's influence and the macroeconomics also affect it. From the angle of the industry, the result can also determine the risk deviation scope in the grey risk control process which offers new content and ideas within the grey risk control.

Under the guidance of the principle of “differential treatment, differential control”, this research will help to strengthen the implementation of differentiated credit policy, focus on guiding and promoting the optimization of credit structure, so as to maintain a reasonable size of credit facilities and build a steady currency credit system.

The paper succeeds in finding the top five influent industries compared with others by using one of the newest developed theories: grey systems theory.