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The purpose of this paper is to solve the dilemma in the process of major selection decision-making.

Firstly, the group of weight vector with kernel has been defined. Then, the weighted comprehensive clustering coefficient vector was calculated based on the group of weight vector with kernel. Under the action of weighted comprehensive clustering coefficient vector, the information including in other components around component k and supporting object i to be classified into the k-th category has been gathered to component k. At last, a novel two-stage decision model based on the group of weight vector with kernel and the weighted comprehensive clustering coefficient vector is put forward to solve the dilemma in grey clustering evaluation. Then the overall evaluation conclusion can be consistent with the clustering result according to the rule of maximum value.

A new way to solve the dilemma in the process of major selection decision-making has been found. People can obtain a consistent result with two-stage decision model at the case of dilemma. That is, the conclusion of the overall evaluation is consistent with the clustering result according to the rule of maximum value.

Several functional groups of weight vector with kernel have been put forward. The proposed model can solve the clustering dilemma effectively and produce consistent results. A practical application of decision problem to solve the dilemma in supplier evaluation and selection of a key component of large commercial aircraft C919 have been completed by the novel two-stage decision model.

The two-stage decision model, the group of weight vector with kernel and the weighted comprehensive clustering coefficient vector were presented in this paper firstly. People can solve the dilemma in grey clustering evaluation effectively by the novel two-stage decision model based on the group of weight vector with kernel and the weighted comprehensive clustering coefficient vector.

The purpose of this paper is to establish a two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem with three-parameter interval grey number to evaluation of agricultural drought resistance grade of 18 cities in Henan Province.

The clustering process is divided into two stages. In the first stage: Combining variance and time degree, the time weight optimization model is established. Applying the prospect theory, the index weight optimization model is established. Then, with the help of grey possibility function, the first stage of grey cloud clustering evaluation is carried out. In the second stage: the weight vector group of kernel clustering is constructed, and the grey class of the object is determined. A two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem is proposed.

This paper indicates that 18 cities in Henan Province are divided into four categories. The drought capacity in Henan province is high in the east and low in the west, high in the south and low in the north and the central region is relatively stable. The drought is greatly affected by natural factors. And the rationality and validity of this model is illustrated by comparing with other methods.

This paper provides a practical method for drought resistance assessment, and provides theoretical support for farmers to grasp the drought information timely and improve the drought resistance ability.

The model in this paper solves the situation of ambiguity and randomness to some extent with the help of grey cloud possibility function. Moreover, the time weight of time degree and variance are used to reduce the volatility and the degree of subjective empowerment. Considering the risk attitude of the decision makers, the prospect theory is applied to make the index weight more objective. 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 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.

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.

According to the grey uncertainty and the connotation of different types weights, the purpose of this paper is to establish the pattern of multi-dimensional grey fuzzy decision making with feedback based on weight vector and weight matrix, and applies this pattern to evaluate the regional financial innovation ability.

At first, this paper analyzes the connotation of financial innovation ability and establishes the evaluation system of regional financial innovation ability. Second, the formula of computing the multi-objective weighted comprehensive value based on weight vector and weight matrix is put forward. In view of the object function with supervised factor and stability coefficient, this paper gives the formulas to compute weight vector and weight matrix. Moreover, the algorithm of the multi-dimensional grey fuzzy decision making pattern with feedback based on weight vector and weight matrix is expressed. At last, this paper uses the presented pattern to evaluate the financial innovation ability of thirty-one provinces in China.

The results are convincing: the development of regional financial innovation is not balanced in China, having obvious spatial clustering feature. The comparisons of evaluation results based on different forms of weights show that the calculating convergence speed of the pattern presented in this paper is fast. The pattern enhances the rationality of the demarcation point between categories, and the convergence within categories, making the evaluation more reasonable.

The method exposed in the paper can be used at evaluating the regional financial innovation ability and even for other similar evaluation problem.

The paper succeeds in realising both the pattern of multi-dimensional grey fuzzy decision making with feedback and evaluating the regional financial innovation ability by using the newest developed theories: weighted grey and fuzzy recognition theory based on weight vector and weight matrix.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.

This study aims to investigate the vulnerability of cold chain logistics through a comprehensive assessment and provide targeted control measures.

The index system of the cold chain vulnerability assessment was established with knowledge obtained from three different dimensions, namely, exposure, sensitivity and adaptability. The final index weight was determined through combination of the intuitionistic fuzzy (IF) entropy and compromise ratio approaches, followed by the comprehensive vulnerability assessment through the two-stage grey comprehensive measurement model. The feasibility and effectiveness of the proposed method were verified by evaluation with SF, HNA, China Merchants and COFCO as target examples.

The results revealed that the most influential factors in the cold chain vulnerability problem were the temperature reaching the standard, as well as the storage and preservation levels; through their analysis combined with the overall cold chain vulnerability assessment, the targeted control measures were obtained.

Based on the research perspective of cold chain vulnerability assessment, a novel assessment model of cold chain logistics vulnerability was proposed, which is based on IF entropy two-stage grey comprehensive measurement. It provides more powerful theoretical support to improve the quality management of cold chain products.

This paper aims to build an improved grey panel clustering evaluation model and evaluate the comprehensive development potential of industrial economy, society and ecological environment in the Yangtze River Economic Belt of China. The purpose of this study is to provide some theoretical basis and tool support for management departments and relevant researchers engaged in industrial sustainable development.

This study uses the driving force pressure state impact response analysis framework to build a comprehensive evaluation index system. Based on the center point triangle whitening weight function, it classifies the panel grey clustering of improvement time and index weight.

The results show that there are great differences in the level of industrial ecological development in different regions of the Yangtze River Economic Belt, which further illustrates the scientificity and rationality of the evaluation method proposed in this paper.

Due to the industrial ecological development is in a constantly changing state, and the information is uncertain. Whitening weight function is introduced to represent the complete information of relevant data. The industrial ecological evaluation involves a comprehensive complex system, which belongs to the panel data analysis problem. The improved grey panel clustering evaluation model is applied to grade the industrial ecological development level of the Yangtze River Economic Belt. The results have important guiding significance for the balanced development of industrial ecology in the region.

Due to the industrial ecological development is in a constantly changing state, and the information is uncertain. Whitening weight function is introduced to represent the complete information of relevant data. The industrial ecological evaluation involves a comprehensive complex system, which belongs to the panel data analysis problem. In order to improve the effectiveness of industrial ecological evaluation, the improved grey panel clustering evaluation model is applied to grade the industrial ecological development level of the Yangtze River Economic Belt. The results have important guiding significance for the balanced development of industrial ecology in the region.

the new model proposed in this paper complements and improves the grey clustering analysis theory of panel data, that is, aiming at the subjective limitation of using time degree to determine time weight in panel grey clustering, a comprehensive theoretical method for determining time weight is creatively proposed. Combining the DPSIR (Driving force-Pressure-State-Influence-Response) model model with ecological development, a comprehensive evaluation model is constructed to make the evaluation results more authentic and comprehensive.

The possibility function-based grey clustering model has evolved into a complete approach for dealing with uncertainty evaluation problems. Existing models still have problems with the choice dilemma of the maximum criteria and instances when the possibility function may not accurately capture the data's randomness. This study aims to propose a multi-stage skewed grey cloud clustering model that blends grey and randomness to overcome these problems.

First, the skewed grey cloud possibility (SGCP) function is defined, and its digital characteristics demonstrate that a normal cloud is a particular instance of a skewed cloud. Second, the border of the decision paradox of the maximum criterion is established. Third, using the skewed grey cloud kernel weight (SGCKW) transformation as a tool, the multi-stage skewed grey cloud clustering coefficient (SGCCC) vector is calculated and research items are clustered according to this multi-stage SGCCC vector with overall features. Finally, the multi-stage skewed grey cloud clustering model's solution steps are then provided.

The results of applying the model to the assessment of college students' capacity for innovation and entrepreneurship revealed that, in comparison to the traditional grey clustering model and the two-stage grey cloud clustering evaluation model, the proposed model's clustering results have higher identification and stability, which partially resolves the decision paradox of the maximum criterion.

Compared with current models, the proposed model in this study can dynamically depict the clustering process through multi-stage clustering, ensuring the stability and integrity of the clustering results and advancing grey system theory.

Water pipes degrade over time for a variety of pipe-related, soil-related, operational, and environmental factors. Hence, municipalities are necessitated to implement effective maintenance and rehabilitation strategies for water pipes based on reliable deterioration models and cost-effective inspection programs. In the light of foregoing, the paramount objective of this research study is to develop condition assessment and deterioration prediction models for saltwater pipes in Hong Kong.

As a perquisite to the development of condition assessment models, spherical fuzzy analytic hierarchy process (SFAHP) is harnessed to analyze the relative importance weights of deterioration factors. Afterward, the relative importance weights of deterioration factors coupled with their effective values are leveraged using the measurement of alternatives and ranking according to the compromise solution (MARCOS) algorithm to analyze the performance condition of water pipes. A condition rating system is then designed counting on the generalized entropy-based probabilistic fuzzy C means (GEPFCM) algorithm. A set of fourth order multiple regression functions are constructed to capture the degradation trends in condition of pipelines overtime covering their disparate characteristics.

Analytical results demonstrated that the top five influential deterioration factors comprise age, material, traffic, soil corrosivity and material. In addition, it was derived that developed deterioration models accomplished correlation coefficient, mean absolute error and root mean squared error of 0.8, 1.33 and 1.39, respectively.

It can be argued that generated deterioration models can assist municipalities in formulating accurate and cost-effective maintenance, repair and rehabilitation programs.