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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.

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 study the modelling mechanisms of several grey incidence analysis models with great influence, including Deng’s grey incidence model, absolute degree of grey incidence model, slope degree of incidence model, similitude degree of incidence model and closeness degree of incidence model; then analyse the problems to be solved in grey incidence analysis models; and clarify the applicable ranges of commonly used grey incidence models.

The paper comes to conclusions by means of comparable analysis. The authors compare several commonly used grey incidence analysis models, including Deng’s grey incidence model, absolute degree of grey incidence model, slope degree of incidence model, similitude degree of incidence model and closeness degree of incidence model and give several examples to clarify the reasons why quantitative analysis results of different models are not exactly the same.

As the intension of each kind of incidence model is clear and the extension is relatively obscure, grey incidence orders calculated by different incidence models are often different. When making actual decisions, incompatible results may appear. According to different characteristics of extraction, grey incidence analysis models can be divided into three types: incidence model based on closeness perspective, incidence model based on similarity perspective and incidence model based on comprehensive perspective.

The conclusions obtained in this paper can help people avoid some defects in the process of actual selection and choose the better incidence analysis model.

The conclusions can be used as a reference and basis for the selection of grey incidence analysis models, it can help to overcome the defects and shortcomings of models caused by themselves and screen out more excellent analytical models.

The purpose of this paper is to solve the problems existing in traditional grey incidence models and advance several new grey incidence models based on visual angle of similarity and nearness.

Based on the definition of traditional grey incidence models, two novel grey incidence models, grey similar incidence model and grey close incidence model, are studied in this paper. The interrelations and influence can be measured by the new models with different visual angle of similarity and/or nearness, respectively. The grey similar incidence model is used mainly to measure the similitude degree of the geometric patterns of sequence curves. The grey close incidence model is used mainly to measure the nearness of the sequence curves in space. The properties of the new models are discussed. It is proved that the proposed models are simplified methods to calculate the similitude degree and the close degree of grey incidence models.

The results show that the two novel grey incidence models satisfy the grey incidence axiom properly. It is useful to calculate the similitude degree and the close degree of two different sequences, and the process of calculating is easier than with traditional grey incidence models.

The method exposed in the paper can be used to calculate every two sequences. The similitude degree and the close degree of two different sequences can be given out. The method can also be used to rank sequences of more than two.

The paper succeeds in constructing two novel grey incidence models. The properties of novel model are studied and it is undoubtedly a new development in grey systems theory.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

The rise in malaria deaths discloses a decline of global malaria eradication that shows that control measures and fund distribution have missed its right of way. Therefore, the purpose of this paper is to study and evaluate the impact and control of malaria on the independent states of the Sub-Saharan African (SSA) region over the time period of 2010–2017 using Deng’s Grey incidence analysis, absolute degree GIA and second synthetic degree GIA model.

The purposive data sampling is a secondary data from World Developmental Indicators indicating the incidence of new malaria cases (per 1,000 population at risk) for 45 independent states in SSA. GIA models were applied on array sequences into a single relational grade for ranking to be obtained and analyzed to evaluate trend over a predicted period.

Grey relational analysis classifies West Africa as the highly infectious region of malaria incidence having Burkina Faso, Sierra Leone, Ghana, Benin, Liberia and Gambia suffering severely. Also, results indicate Southern Africa to be the least of all affected in the African belt that includes Eswatini, Namibia, Botswana, South Africa and Mozambique. But, predictions revealed that the infection rate is expected to fall in West Africa, whereas the least vulnerable countries will experience a rise in malaria incidence through to the next ten years. Therefore, this study draws the attention of all stakeholders and interest groups to adopt effective policies to fight malaria.

The study is a pioneer to unravel the most vulnerable countries in the SSA region as far as the incidence of new malaria cases is a concern through the use of second synthetic GIA model. The outcome of the study is substantial to direct research funds to control and eliminate malaria.

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 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.

This paper aims to establish a novel three-way decisions-based grey incidence analysis clustering approach and exploit it to extract information and rules implied in panel data.

Because of taking on the spatiotemporal characteristics, panel data can well-describe and depict the systematic and dynamic of the decision objects. However, it is difficult for traditional panel data analysis methods to efficiently extract information and rules implied in panel data. To effectively deal with panel data clustering problem, according to the spatiotemporal characteristics of panel data, from the three dimensions of absolute amount level, increasing amount level and volatility level, the authors define the conception of the comprehensive distance between decision objects, and then construct a novel grey incidence analysis clustering approach for panel data and study its computing mechanism of threshold value by exploiting the thought and method of three-way decisions; finally, the authors take a case of the clustering problems on the regional high-tech industrialization in China to illustrate the validity and rationality of the proposed model.

The results show that the proposed model can objectively determine the threshold value of clustering and achieve the extraction of information and rules inherent in the data panel.

The novel model proposed in the paper can well-describe and resolve panel data clustering problem and efficiently extract information and rules implied in panel data.

The proposed model can deal with panel data clustering problem and realize the extraction of information and rules inherent in the data panel.

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.