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The paper aims to propose a clustering model for panel data. More specifically, the paper aims to construct a gray incidence model for panel data to solve the classification with multi-factors and multi-attributes.

The paper opted for a clustering theory study using gray incidence theory based on dynamic weighted function. The paper presents an example to verify the rationality of the new model, which suggests that the new model can reflect the incidence degree of panel data.

The paper provides a new gray incidence model based on a dynamic weighted function that can amplify the characteristics of the sample to some extent. The properties of the new incidence model, such as normalization, symmetry and nearness, are all satisfied. The paper also shows that the new incidence model performs very well on cluster discrimination.

The new model in this paper has supplemented and improved the gray incidence analysis theory for panel data.

The purpose of this paper is to develop a system to analyse the characteristics of infrared objects.

According to the gray scale of image pixel by the image entropy, gray scale estimating is carries on to construct the neural networks. And then the grey relational analysis and grey clustering methods are applied to filter the possible object. The target is predicted through image segmentation pretreatment based on the forecasting value by grey system and assigned corresponding mark. The forecasting precision is greatly elevated by GM (1, 1) model.

The paper illustrates that, based on the analysis and its experimental results, this system has a good recognition rate for infrared target.

This paper provides a way to grasp the minutial feature of the image. The filtering operation based on pixel level provided auto‐adapted filtering with a new stage.

Applications of grey theory deepened the content of detecting infrared targets and enriched technology of image processing.

This system introduces an effective method for detecting infrared targets.

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.

This paper aims to evaluate the stage and level of Henan province urbanization and provide basis for decision making.

At first, build the evaluation index system which includes 17 indexes in four classes so that can reflect the level of urbanization development of the entire region comprehensively. Then build the gray clustering model based on set pair. On this basis, the paper evaluates the urbanization process in Henan province. In order to get a clear understanding of the urbanization level in Henan province, the paper selects several typical provinces and compares them with Henan province in urbanization process.

The results show that the urbanization level in Henan province belongs to the general level; there is a gap in urbanization process between Henan province and other advanced provinces.

The paper put forward a method to evaluate the urbanization process in Henan province and get a clear understanding of the urbanization level in Henan province.

The paper combines the set pair analysis and the gray fixed weight cluster method based on triangular whiten weight function, which can avoid the defect that the assessment result is too vague and the difference is not significant.

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.

Grey modeling technique is an important element of grey system theory, and academic articles applied to agricultural science research have been published since 1985, proving the broad applicability and effectiveness of the technique from different aspects and providing a new means to solve agricultural science problems. The analysis of the connotation and trend of the application of grey modeling technique in agricultural science research contributes to the enrichment of grey technique and the development of agricultural science in multiple dimensions.

Based on the relevant literature selected from China National Knowledge Infrastructure, the Web of Science, SpiScholar and other databases in the past 37 years (1985–2021), this paper firstly applied the bibliometric method to quantitatively visualize and systematically analyze the trend of publication, productive author, productive institution, and highly cited literature. Then, the literature is combed by the application of different grey modeling techniques in agricultural science research, and the literature research progress is systematically analyzed.

The results show that grey model technology has broad prospects in the field of agricultural science research. Agricultural universities and research institutes are the main research forces in the application of grey model technology in agricultural science research, and have certain inheritance. The application of grey model technology in agricultural science research has wide applicability and precise practicability.

By analyzing and summarizing the application trend of grey model technology in agricultural science research, the research hotspot, research frontier and valuable research directions of grey model technology in agricultural science research can be more clearly grasped.

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 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.

The purpose of this research is to provide a theoretical framework for complex equipment quality risk evaluation. The primary aim of the framework is to enhance the ability to identify risks and improve risk control efficiency during the development phase.

A novel framework for quality risk evaluation in complex equipment is proposed, which integrates probabilistic hesitant fuzzy set-quality function deployment (PHFS-QFD) and grey clustering. PHFS-QFD is applied to identify the quality risk factors, and grey clustering is used to evaluate quality risks in cases of poor quality information during the development stage. The unfolding function of QFD is applied to simplify complex evaluation problems.

The methodology presents an innovative approach to quality risk evaluation for complex equipment development. The case analysis demonstrates that this method can efficiently evaluate the quality risks for aircraft development and systematically trace back the risk factors through hierarchical relationships. In comparison to traditional failure mode and effects analysis methods for quality risk assessment, this approach exhibits superior effectiveness and reliability in managing quality risks for complex equipment development.

This study contributes to the field by introducing a novel theoretical framework that combines PHFS-QFD and grey clustering. The integration of these approaches significantly improves the quality risk evaluation process for complex equipment development, overcoming challenges related to data scarcity and simplifying the assessment of intricate systems.

The purpose of this paper is to design an inference engine to measure the level of readiness of each bank before starting the corporate sustainability auditing process. Based on the output of the designed inference engine, the audition team can decide about the audition resources and the auditing process.

In this paper, the hybrid rough and grey set theory are used to design and create a rule model system to measure the sustainability level of banks. First, 16 rule models are extracted using rough set theory (RST), and the cross-validation of each model is done. Then, the grey clustering is used to combine the same condition attributes and improve the validity of the final model. A total of 16 new rule models are extracted based on the decreased condition attributes, and the best model is selected based on the cross-validation results.

By comparing the accuracy of rough-gray’s rule models and as a result of decreasing the condition attributes, a proper increase in the accuracy of all models is obtained. Finally, the Naive/Genetic/object-related reducts model with 95.6% accuracy is selected as an inference engine to measure new banks’ readiness level.

Sustainability measurement of banks based on RST is a new approach in the field of corporate sustainability. Furthermore, using the grey clustering for combining the condition attributes is a novel solution for improving the accuracy of the rule models.