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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 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.

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.

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 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 explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

PHYSICISTS are well acquainted with the relationship which exists between naval and the aeronautical problems. Although the specific gravity of water is a thousand times greater than that of air, the similitude in their flow goes beyond the limits of mathematical analysis; but experiments in water, which have the advantage of being easy of application, although requiring certain precautions, have yielded a number of conclusions that have proved useful in the case of sections and other component parts of aeroplanes.

No matter in product design stage or product quality improvement stage, the product technical requirements (PTRs) impacting on product performance are mainly identified and improved to optimize customer needs (CNs) as greatly as possible. The purpose of this paper is to use a new approach to accurately and properly prioritize PTRs in Quality Function Deployment (QFD).

Considering the relationship between CNs and PTRs in QFD hard to quantitatively measure and lack of adequate information, the grey relational analysis (GRA) is applied. Besides, owing to the inherent inner dependencies of CNs as well as QFD, the analytic network process (ANP) which is an effective tool to take into account the inner dependencies with network is utilized. Finally, an integrated framework based on GRA method and ANP approach is proposed to determine the importance degrees of PTRs in designing a product.

The calculation results of the application show that the proposed framework by integrating GRA and ANP is able to determine the importance degrees of PTRs in design a product well.

In the application part the authors can see the proposed framework can be applied to PVC window systems. Owing to that traditional QFD method has been widely used in many fields such as manufacturing industry and service industry, actually the proposed framework has great potential application in the real word.

This paper succeeds in proposing a new framework by integrating GRA and ANP to determine the importance degrees of PTRs in QFD.

Under this heading are published regularly abstracts of all Reports and Memoranda of the Aeronautical Research Council, Reports and Technical Notes of the United States National Advisory Committee for Aeronautics and publications of other similar Research Bodies as issued