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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.

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.

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.

The purpose of this paper is to propose a grey clustering evaluation model based on analytic hierarchy process (AHP) and interval grey number (IGN) to solve the clustering evaluation problem with IGNs.

First, the centre-point triangular whitenisation weight function with real numbers is built, and then by using interval mean function, the whitenisation weight function is extended to IGNs. The weights of evaluation indexes are determined by AHP. Finally, this model is used to evaluate the flight safety of a Chinese airline. The results indicate that the model is effective and reasonable.

When IGN meets certain conditions, the centre-point triangular whitenisation weight function based on IGN is not multiple-cross and it is normative. It provides a certain standard and basis for obtaining the effective evaluation indexes and determining the scientific evaluation of the grey class.

The traditional grey clustering model is extended to the field of IGN. It can make full use of all the information of the IGN, so the result of the evaluation is more objective and reasonable, which provides supports for solving practical problems.

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 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.

The purpose of this paper is to attempt to establish a grey clustering evaluation model of center-point triangular whitenization weight function to measure the performance of enterprise's management innovation (MI). The author intends to provide some theory basis and tool support for enterprise's managers and other researchers who are engaged in performance measuring.

The study uses questionnaire survey and expert interviews to determine the index weight of enterprise's MI performance (MIP), classifies the grey clusters based on center-point triangular whitenization weight function, calculates the membership of performance criteria and ranks the performance level of all dimensions.

The survey data of case company shows that production performance is in superior level, employee and society influence performance are in satisfied level, finance and market performance are in intermediate level, total MIP is in satisfied level.

MI is the fundamental way to keep enterprise's core competitiveness and achieve its strategic objectives. Performance is an effective tool to measure the MI. Therefore, based on the practices of MI in China, the study systematically clarifies the performance level of MI from five dimensions.

The evaluation index of enterprise's MIP is built with five dimensions which contain production, market, finance, employee and social influence. The grey clustering evaluation model based on triangular whitenization weight function is applied to assess the performance criteria. This paper presents a new research idea for enterprise's performance evaluation.

The purpose of this paper is to propose a multi-scale extended grey target decision method for dealing with multi-attribute decision-making problems with interval grey numbers whose value distribution information is asymmetrical.

First, the whitenization weight function (WWF) was adopted to show the value distribution information of interval grey numbers. The definitions of kernel, degree of greyness, relative kernel and whitenization standard deviation of interval grey numbers were given based on the WWF. Then, the relative kernel grey target and whitenization standard deviation grey target were constructed to take full advantage of the owned decision information. Finally, the relative bull’s-eye coefficient was proposed to rank the preference order of all alternatives.

The relative bull’s-eye coefficient reflects the influence of the decision information on decision results with respect to the mean level and value distribution of attribute values. Thus, the decision-maker could set the return and risk adjustment coefficient according to their preferences and select the optimal alternative with a high expected return and low risk.

The paper considers the valve distribution information of interval grey numbers, and a novel definition for kernels, degrees of greyness, relative kernels and whitenization standard deviations, which are given based on the WWF. The paper not only considers the influence of mean levels of decision information over decision results, but also takes the value distribution information into account.

The time required for a certain task to be performed normally reduces on its frequent completion, as more units are produced over time, it is expected to have an increase in the total worker’s output performance. Learning curve (LC) is a mathematical representation to estimate the time of tasks which occurs repeatedly. The parameter prediction is considered a major disadvantage from which LC suffers. The purpose of this paper is to investigate grey systems theory as a method for the standard time.

The proposed method starts with data which are obtained by traditional time study and then, models LC for an assembling activity of Electrogen Company. The paper studies the grey evaluation method based on triangular whitenization weight functions which includes two classes: endpoint triangular whitenization functions and center-point triangular whitenization functions. The grey system results are compared with those of the LC.

The results show that the standard time given by grey systems theory is closer than the standard time given by LC to standard time with 100 per cent performance level.

Scheduling problems are complex and uncertain, and it is very rare for such systems to be exactly determined in all their complexity. According to grey systems theory, the job processing time can be considered as the object that extension is definite but intension is uncertain. Consequently, grey systems theory with its focus on the uncertainty problems of small samples and incomplete information is proposed in the paper.

This paper aims to investigate the performance of Jiangsu Province industrial technology innovation strategy alliance.

Through a preliminary investigation of 30 Jiangsu industrial technology innovation strategic alliances, this paper analyzed the status and extracted 18 alliances to conduct an in-depth investigation. By grey evaluation method based on center-point triangular whitenization weight function, the paper classified and analyzed alliances.

The results show that university or research institutions-oriented alliance perform better, but the government/enterprise-oriented alliance perform diverse, and majority is rated “general”.

The paper succeeds in clustering analysis to Jiangsu Province industrial technology innovation strategy alliance with insufficient data. And according to the result of clustering, it analyzes the causes, which provide value information for the sustainable development of Jiangsu Province industrial technology innovation strategy alliance.