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The purpose of this paper is to find the reason which the results of grey variable weight clustering method do not correspond with the reality. It proposes reconstructing the whitenization weight function, outlining why and how inconsistency is avoided. The study aims to improve the model of grey clustering method based on the whitenization weight function and list the steps of the new clustering model so that analysis and application of innovation capacity in a broader range is normally found.

First the reason for the problem that the clustering results of grey variable weight clustering do not correspond with the reality is analyzed in two existing literature. And then a new whitenization weight function is reconstructed, two properties of the whitenization weight function are proved. The solution of the new grey variable weight clustering based on the whitenization weight function is built by following six steps.

The paper provides a new whitenization weight function which satisfies the normative and non-triplecrossing. It suggests that successful clustering results of innovation capacity act on two levels: integrating the elements of innovation capacity indexes, and following steps of grey variable weight clustering.

This paper improves the existing method of grey variable weight clustering and fulfills an identified need to study how cities’ innovation capacity can be clustered.

The purpose of this paper is to propose a grey clustering model based on kernel and information field to deal with the situation in which both the observation values and the turning points of the whitenization weight function are interval grey numbers.

First, the “unreduced axiom of degree of greyness” was expanded to obtain the inference of “information field not-reducing”. Then, based on the theoretical basis of inference, the expression of whitenization weight function with interval grey number was provided. The grey clustering model and fuzzy clustering model were compared to analyse the relationship and difference between the two models. Finally, the paper model and the fuzzy clustering model were applied to the example analysis, and the interval grey number clustering model was established to analyse the influencing factors of regional drought disaster risk in Henan Province.

The example analysis results illustrate that although the two clustering methods have different theoretical basis, they are suitable for dealing with complex systems with uncertainty or grey characteristic, solving the problem of incomplete system information, which has certain feasibility and rationality. The clustering results of case study show that five influencing factors of regional drought disaster risk in Henan Province are divided into three classes, consistent with the actual situation, and they show the validity and practicability of the clustering model.

The paper proposes a new whitenization weight function with interval grey number that can transform interval grey number operations into real number operations. It not only simplifies the calculation steps, but it has a great significance for the “small data sets and poor information” grey system and has a universal applicability.

The purpose of this paper is to cluster and analyse the level of agricultural science and technology in China’s provinces by using grey clustering model, to have an overall understanding of the current situation of agricultural science and technology development in these provinces, and to offer a reference for decision-making departments to draw up agricultural science and technology development plans.

First of all, the grey clustering assessment is used to evaluate the clustering of agricultural science and technology level in China’s provinces in 2011, 2013 and 2015. Also a comparative static analysis is made. Then, based on the prediction data of GM (1,1) model, the provincial agricultural science and technology levels in 2017 and 2019 are analysed by grey clustering. Finally, some suggestions are put forward, such as adjusting the allocation of agricultural science and technology resources and providing policy preferences to backward areas, so as to promote the coordinated development of agricultural science and technology in China.

The development of agricultural science and technology in various provinces and regions of the authors’ country is unbalanced, with a big gap of agricultural and technology level between different provinces. What’s more, the level of agricultural science and technology in remote areas has been developing slowly, but it has been lagging behind. Through the grey clustering analysis of the provincial agricultural science and technology level in 2017 and 2019, it is concluded that the level of agricultural science and technology will be promoted as a whole, but the gap of agricultural science and technology level between different provinces and cities will be enlarged.

This paper comprehensively studies the current situation and future development trends of agricultural science and technology in China’s provinces in recent years, and preliminarily analyses the reasons for the transformation of agricultural science and technology level, however, with no further inspection. Related research should be made for further study.

This paper will provide overall understanding of the current situation of agricultural science and technology development in China’s provinces and cities, and put forward relevant suggestions for the future development of agricultural science and technology in China’s provinces and cities, and provide references for decision-making departments to draw up agricultural science and technology development plans.

For the first time, the grey clustering method is used to the research of agricultural science and technology level in the province. It analyses and evaluates the past and present situation and predicts the future development trend of provincial agricultural science and technology level by the grey clustering analysis method, which is a complete research.

In multi-criteria decision-making with interval grey number information, decision makers usually take a risk to rank or choose some very similar alternatives. Additionally, when evaluating only one alternative, decision makers can only obtain a specific value using traditional decision-making methods and may find it hard to cluster the alternatives to the “correct class” because these methods lack predetermined reference points. To overcome this problem, this paper aims to propose a two-stage grey decision-making method.

First, a new type of clustering method for interval grey numbers is designed by proposing a new possibility function for grey numbers. Based on this clustering method, a new grey clustering evaluation model for interval grey numbers is proposed by which decision makers can obtain the grade rating information of each alternative. Then, according to the grey clustering evaluation model, a new two-stage decision-making method is introduced to solve the problem that some alternatives are very similar by designing a grey comprehensive decision coefficient of alternatives.

The authors propose a new grey clustering evaluation model to deal with interval grey numbers. They design a new model to obtain the membership degree for the interval grey numbers and then propose a new grey clustering evaluation model, which can evaluate only one alternative by predefined grey classes. Then, by the grey comprehensive decision coefficient, a two-stage grey evaluation decision-making method is put forward to solve the problem that some alternatives are very close and hard to be distinguished.

A new grey clustering evaluation model is proposed, which can evaluate only one alternative by predefined grey classes. A two-stage grey evaluation decision-making method is given to solve the problem that some alternatives are very close and hard to be distinguished.

The purpose of this paper is to establish a two-stage grey cloud clustering model to assess the drought risk level of 18 prefecture-level cities in Henan Province.

The clustering process is divided into two stages. In the first stage, grey cloud clustering coefficient vectors are obtained by grey cloud clustering. In the second stage, with the help of the weight kernel clustering function, the general representation of the weight vector group of kernel clustering is given. And a new coefficient vector of kernel clustering that integrates the support factors of the adjacent components was obtained in this stage. The entropy resolution coefficient of grey cloud clustering coefficient vector is set as the demarcation line of the two stages, and a two-stage grey cloud clustering model, which combines grey and randomness, is proposed.

This paper demonstrates that 18 cities in Henan Province are divided into five categories, which are in accordance with five drought hazard levels. And the rationality and validity of this model is illustrated by comparing with other methods.

This paper provides a practical and effective new method for drought risk assessment and, then, provides theoretical support for the government and production departments to master drought information and formulate disaster prevention and mitigation measures.

The model in this paper not only solves the problem that the result and the rule of individual subjective judgment are always inconsistent owing to not fully considering the randomness of the possibility function, but also solves the problem that it’s difficult to ascertain the attribution of decision objects, when several components of grey clustering coefficient vector tend to be balanced. It provides a new idea for the development of the grey clustering model. The rationality and validity of the model are illustrated by taking 18 cities in Henan Province as examples.

The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster evaluation models.

In this paper, the triangular whitenization weight function corresponding to class 1 is changed to a whitenization weight function of its lower measures, and the triangular whitenization weight function corresponding to class s is changed to a whitenization weight function of its upper measures. The difficulty in extending the bound of each clustering indicator is solved with this improvement.

The findings of this paper are the novel grey cluster evaluation models based on mixed centre-point triangular whitenization weight functions and the novel grey cluster evaluation models based on mixed end-point triangular whitenization weight functions.

A practical evaluation and decision problem for some projects in a university has been studied using the new triangular whitenization weight function.

Particularly, compared with grey variable weight clustering model and grey fixed weight clustering model, the grey cluster evaluation model using whitenization weight function is more suitable to be used to solve the problem of poor information clustering evaluation. The grey cluster evaluation model using endpoint triangular whitenization weight functions is suitable for the situation that all grey boundary is clear, but the most likely points belonging to each grey class are unknown; the grey cluster evaluation model using centre-point triangular whitenization weight functions is suitable for those problems where it is easier to judge the most likely points belonging to each grey class, but the grey boundary is not clear.

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.

With the improvement of economic level, car ownership is growing, and the number of scrapped automobiles is increasing. Therefore, evaluation research for auto parts remanufacturing is particularly important. The purpose of this paper is to construct the evaluation index system of auto parts remanufacturing and research the grey clustering theory. The grey fixed weight clustering evaluation is used to evaluate automobile engine remanufacturability.

According to the policies and regulations of China about remanufacturing, economic, technical, resources, energy and the environment, four indexes are selected to set up the evaluation standard of auto parts remanufacturing scheme. Grey fixed weight clustering method is used to evaluate remanufacturability of the auto parts. Firstly, number index and grey determine the whitenization weight function, then based on the clustering weight of each index, the clustering coefficient matrix is calculated. Finally, the class that certain object belongs to, according to the clustering coefficient matrix is determined.

Results show that constructed indexes of auto parts remanufacturing scheme can be used for effective evaluation. And the proposed fixed weight grey cluster model can aggregate all indexes information well. Therefore, the proposed indexes and model in this paper are effective and can be used for auto parts remanufacturing.

According to the requirements of the current situation in China, this paper puts forward a method based on grey clustering decision, to evaluate different auto parts remanufacturing schemes, for manufacturing enterprises to provide theoretical basis for remanufacturing production, in order to realize the reasonable configuration of resources.

This paper firstly establishes the evaluation index system of auto parts remanufacturing, the grey clustering theory is introduced into the evaluation of remanufacturing. The fixed-weight grey cluster model is proposed to aggregate indexes’ information.

The purpose of this paper is to establish a grey clustering evaluation model based on center-point triangular whitenization weight function to evaluate the situation of urban low-carbon transport development (LTD). The study results intend to provide some theoretical basis and tool support for transport management departments and related researchers who are engaged in low-carbon transport (LT).

The study uses analytical hierarchy process based on expert investigations to determine the weight of each criteria, classifies the grey clusters based on center-point triangular whitenization weight function, calculates the membership of each development criteria and ranks the development level of all dimensions.

The research results of case city show that low-carbon technology is in “poor” level, transport facility is in “superior” level, low-carbon policy and environmental coordination is in “intermediate” level, transport management is in “good” level and the overall LTD level is in “intermediate” level.

Reducing the carbon emissions of urban transport and achieving LT is the key to promote urban sustainable development, the scientific judgment of transport development situation is the premise of promoting LTD. Therefore, based on the practices of LT in China, the study systematically clarifies LTD from five dimensions of reflecting LTD.

From the perspective of sustainable development, the evaluation index system of LTD is built with five dimensions consisting of low-carbon technology, low-carbon policy, transport facility, transport management and environmental coordination. Then assess the LTD by using the grey clustering evaluation model based on center-point triangular whitenization weight. This paper presents a new research idea for LTD evaluation.

Nowadays, evaluation objects are becoming more and more complicated. The interval grey numbers can be used to more accurately express the evaluation objects. However, the information distribution of interval grey numbers is not balanced. The purpose of this paper is to introduce the central-point triangular whitenization weight function to solve the clustering process of this kind of numbers.

A new expression of the central-point triangular whitenization weight function is presented in this paper, in terms of the grey cluster problem based on interval grey numbers. By establishing the integral mean value function on the set of interval grey numbers, the application range of grey clustering model is extended to the interval grey number category, and, in this way, the grey fixed weight cluster model based on interval grey numbers is obtained.

The model is verified by a case which reveals a high distinguishability, validity and practicability.

This model can be used in many fields, such as agriculture, economy, geology and medical science, and provides a feasible method for evaluation schemes in performance evaluation, scheme selection, risk evaluation and so on.

The central-point triangular whitenization weight function is introduced. The method reflects the thought “make full use of the information” in grey system theory and further enriches the system of grey clustering theory as well as expands the application scope of the grey clustering method.