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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.

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 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 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 purpose of this paper is to evaluate, analyse and select the best suppliers for Satrec Vitalait Milk Company, operating in Senegal, based on criteria obtained from economic, environmental and social dimensions of sustainable supply chain management, through the application of Deng’s grey relational analysis (GRA) model, absolute GRA model (ADGRA) and a novel second synthetic GRA (SSGRA) model, combined with one decision making under the uncertainty-based model, namely, the Hurwicz criteria.

The research adopts a new synthetic GRA model and highlights its reliability on small sample gathered from four senior experts of the company who administered a total number of 28 specialists operating in four departments of the company, through the employment of a self-administered questionnaire designed based on criteria identified from the literature that were refined via a Q-sort model.

The outcomes of the research methodology designated that all the selected five suppliers present a degree of attaining sustainability due to the fact that supplying unprocessed milk does not require the use of polluting methods for stocking and transportation. The undertaken study specifies that all the socio-environmental criteria play a crucial role in shaping the sustainability level of Satrec Vitalait’s suppliers and demonstrates the accuracy of the results obtained through the second synthetic degree of grey relation analysis for ranking the suppliers. Supplier 2 was found to be the best supplier for the company and, as result, a model for other suppliers to mimic.

Future researchers can replicate the GRA-based supply chain model proposed in the current study in different environments especially in the context of green supply chain. Also, in future the SSGRA model, while using the bidirectional ADGRA instead of the conventional ADGRA, should also be tested, especially when the data sequences associated with different supply chain parameters have inconsistent directions. Also, comparative analysis of SSGRA-based results with that of modern statistical methods like structural equation modelling can also be used for future explorations. Furthermore, the current study is built upon the data associated with the Satrec Vitalait Milk Company (Senegal); therefore, the findings should be generalised with caution.

The study can be seen as a first-stepping stone for gauging and selecting the best sustainable supplier for Satrec Vitalait using grey system theory. For purpose of attaining the research goal, the SSGRA was exploited as an innovative experimental approach to estimate relationships between criteria with regard to the sustainability level of the company’s suppliers. Under this scope, relationships between criteria themselves and their goal were depicted by Deng’s degree of GRA and AGRA, respectively. The research is innovative by means of the framework of its methodology and data analysis.

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.

The identification of the main risk triggers is essential for the hospital’s survival and performance with direct effects on its patients’ health and well-being. For this reason, in this paper some of the most important risk categories have been determined. While in a previous research a qualitative analysis has been done for determining which are the most important risks felt by the patient that are believed to affect their health through the usage of a questionnaire and through conducting a confirmatory factor analysis, the purpose of this paper is to analyze the quantitative side of these risks’ presence in a hospital.

On this purpose, four main categories of risks have been considered (the same as in the qualitative research) and they have been analyzed from the hospital’s point of view – through the usage of the hospital financial and internal documents. Therefore, a series of indicators have been determined for each risk category. After that, a representative indicator has been selected and the grey incidence analysis has been conducted.

By comparing the results gathered form this study with the qualitative analysis conducted among the patients (Delcea et al., 2016) it can be said that there can be seen a difference among the way a hospital and a patient perceive the risks within a medical activity. While for the hospital, the most affecting risk is the technological and hospital conditions risk, for the patients the most affecting risk seems to be the human resources and clinical risk. The mismanagement risk and inability to treat patients is the second in intensity for both the hospital and patients, with a smaller value in the patients’ case.

From here, the research can be extended for capturing the risks that are considered to be important for the medical stuff, which will permit us to have a global image over the healthcare risks. After that, a comparative analysis among the hospitals with different financial performance can be conducted in order to see how these risks are affecting their performance and to determine which can be the decisions that can fostering the reduction of these risks.

The present paper offers a quantitative analysis from the hospital’s point of view using the advantages offered by the grey systems theory. Combining this analysis with a qualitative one conducted on the patients, the managers of the hospital can a have a more adequate view over the risks that they are facing with. In this context, grey systems theory offers the needed methods for dealing with such situations.

The knowledge of goals of the successor, who is preparing to take over the business, is extremely important for the succession process and further operation of a family enterprise. The aim of this study is to structure the goals of Polish family enterprises’ successors and to develop a Synthetic Model of the goals of Polish family enterprises' successors with the application of grey clustering evaluation models.

Research into the specifics of the diagnosis and assessment of the goals set for the successors of the first succession in family businesses in Poland was carried out in the third quarter of 2016 at two stages using two research methods: in-depth group interview and individual interview. The main aim of the first stage was the extraction of subjectively identified goals by family enterprises' successors (based on their succession experience). The statements were open and obtained during two in-depth group interviews (2 FGI) with successors being in the process of succession at its various stages (total, n = 14). The respondents presented their experiences connected with the succession process along with emotions that are associated with it. In one of the interview stages, the respondents were asked to enumerate their individual goals they set for themselves in the context of upcoming changes. Next, the group agreed on the most frequently mentioned goals by creating their verbal interpretation. The obtained list of 20 goals was recorded and discussed, and thanks to the application of the elimination rule in the collective decision-making process, that list was reduced to 10 goals, which was approved by all participating successors.

The results show the developed Synthetic Model of the goals of family enterprises’ successors. The study singled out four groups of successors: (1) successors who do not work in the family enterprise yet, (2) successors holding lower-level positions, (3) successors holding managerial positions, (4) successors who manage the entire company. As a result of the calculations, the developed Synthetic Model of the goals of family enterprises' successors was positively verified for successors working in higher-level positions and successors managing the entire family enterprise.

In order to use the results of clustering, e.g. for conducting studies on large samples with the use of statistical tools, a reduced number of goals should be taken into account. A thorough study of three goals may bring results similar to the study of the original ten successors of Polish family enterprises in the process of succession. The aim of future research is to develop a mathematical model using optimization functions that enable selection of elements representing individual clusters in such a way that it leads to the extraction of the elements with the highest value in relation to the accepted criterion for assessing their value.

In the future, conducting family business research in accordance with the developed methodology requires a look at the proposed list of successor goals obtained during the Focus Group Interview (FGI) as it could be shortened using the Cluster of Grey Incidence method. Shortening the list of goals has its analytic and practical justifications. The study of the full list of goals in subsequent (and numerous further studies) could lead to errors related to, for example, different interpretation of goals among the investigated successors. Furthermore, the full list of goals would increase costs and extend research time.

The purpose of this paper is to realize dynamical grey incidence order of influencing factors of grain production in Henan province using grey systems theory.

Starting from choosing influence factors on grain production and dividing the 30 years (from 1979 to 2009 year) of grain production in Henan province into three periods, the authors calculate grey incidence degree between grain yield and every influencing factor by grey incidence analysis method, respectively, then obtain the grey incidence order of influencing factors in every period. Also based on the three grey incidence orders from different periods, the authors find a changeable tendency of influencing factors on grain production and key influencing factors on grain production in different periods. Finally, to keep Henan province grain production stable and sustainable, several policy suggestions are given.

The results are convincing: it is effective and powerful to analyze dynamically influencing factors of grain production using grey systems theory, and it is urgent to strengthen agricultural science and technology input, and pay close attention to the influence of dosage of pesticide and fertilizers on grain production.

Grey incidence analysis and findings exposed in the paper can be used by agricultural firms to optimize grain production plans, and by government to formulate reasonable agricultural production policies.

The paper succeeds in getting dynamical grey incidence order of influencing factors of grain production in Henan province using grey systems theory.