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The purpose of this work is to construct a grey entropy comprehensive evaluation model to measure the regional green innovation vitality (GIV) of 31 provinces in China.

The traditional grey relational proximity and grey relational similarity degree are integrated into the novel comprehensive grey evaluation framework. The evaluation system of regional green innovation vitality is constructed from three dimensions: economic development vitality, innovative transformation power and environmental protection efficacy. The weights of each indicator are obtained by the entropy weight method. The GIV of 31 provinces in China is measured based on provincial panel data from 2016 to 2020. The ward clustering and K-nearest-neighbor (KNN) algorithms are utilized to explore the regional green innovation discrepancies and promotion paths.

The novel grey evaluation method exhibits stronger ability to capture intrinsic patterns compared with two separate traditional grey relational models. Green innovation vitality shows obvious regional discrepancies. The Matthew effect of China's regional GIV is obvious, showing a basic trend of strong in the eastern but weak in the western areas. The comprehensive innovation vitality of economically developed provinces exhibits steady increasing trend year by year, while the innovation vitality of less developed regions shows an overall steady state of no fluctuation.

The grey entropy comprehensive relational model in this study is applied for the measurement and evaluation of regional GIV, which improves the one-sidedness of traditional grey relational analysis on the proximity or similarity among sequences. In addition, a three-dimensional evaluation system of regional GIV is constructed, which provides the practical guidance for the research of regional development strategic planning as well as promotion paths.

A comprehensive grey entropy relational model based on traditional grey incidence analysis (GIA) in terms of proximity and similarity is proposed. The three-dimensional evaluation system of China's regional GIV is constructed, which provides a new research perspective for regional innovation evaluation and expands the application scope of grey system theory.

The hotel and tourism industry forms a crucial economic sector for all the economies around the world. However, it suffered the worst hit during the COVID-19 outbreak. Considering the hotel and tourism sector's critical situation, this manuscript aims to emphasise the importance of resilience in the hotel and tourism supply chain (HTSC) and explores the crucial barriers that tend to disturb the inculcation of stability in the hotel and tourism sector. The present research analyses the factors influencing the hotel and tourism sector's resilience and also takes into consideration the various critical success factors (CSFs) needed to build a resilient HTSC.

A two-phase research approach has been proposed and used in this study. In the first phase, eight CSFs and sixteen factors influencing the hotel and tourism sector's resilience during the COVID-19 pandemic were identified. The basis of the identification of the CSFs and factors was literature and inputs received from experts. In the second phase, the grey-Entropy-EDAS, a qualitative and quantitative analysis, was used to analyse the identified CSFs and factors to determine the priority of concern.

In this research, the most imperative facet influencing the hotel and tourism sector's resilience has been identified, and the findings will assist hotel and tourism sector in managing and mitigating the repercussions of the COVID-19 pandemic. The analysis of the results indicates that out of all the critical success factors, supply chain visibility is the most crucial aspect in building HTSC's resilience, whereas economic catastrophe is the most influential factor. Sensitivity analysis is also conducted to examine the priority ranking stability.

The results of this study can be used by the hotel supply chain managers and policymakers to plan for various challenges faced by them as they try to implement resilience-based strategies in their supply chain.

This research is unique as it analyses the general factors hindering the pathway of resilience in the hotel and tourism supply chain. This is also the first kind of study that has used grey-Entropy to analyse the critical success factors and grey-EDAS for analysing the impact of various factors influencing the hotel and tourism sector's resilience.

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications, which include ordinal grey relational grade and cardinal grey relational grade. However, the most original and important formula is Deng’s grey relational grade. After careful study it was found that although it is an ordinal form of grey relational grade, a rational mathematics model can be used to transfer it from ordinal into cardinal. It not only can enhance the essential of Deng’s grey relational grade, but also can let Deng’s grey relational grade be used more widely. The paper aims to discuss these issue.

The paper uses fuzzy set theory to get the rational value of distinguish coefficient in Deng’s grey relational grade, then uses grey entropy method to decide the rational weighting for the analysis sequences in Deng’s grey relational grade.

Through the mathematics derivation, it indeed can transfer the Deng’s grey relational grade from ordinal form into cardinal form.

The paper has deeply enhanced the essential of Deng’s grey relational grade, and made Deng’s grey relational grade more available and more usable in grey system theory.

The paper has transferred the Deng’s grey relational grade from ordinal into cardinal, it can let Deng’s grey relational grade be used in a wider area.

The purpose of this paper is to explore the method of clinical department classification in comprehensive hospital to provide a scientific management reference in performance evaluation.

In order to perform the classification of clinical departments, a grey cluster model was constructed. In this model, the benefit index of each clinical department was analyzed using grey associative analysis, and a superior index was chosen to incorporate in this model. Through the relevancy degree of superior index, the authors confirmed the weight of index, and the quintile threshold was calculated by a quintile method and whitening weight functions were constructed.

This model, based on grey entropy weight cluster, can reasonably distinguish the merits of clinical departments. From the case we study, neurology?/Cardiovasology?/Integrated disease and Emergency were the optimum assessing department.

The results demonstrated that the index selection, weight determination, whitening weight functions and model construction in this study could provide technique’s reference and application for hospital administrators. It avoids the subjective discrimination and reduces the influence of sample noise, and it is easy to perform while conducting performance evaluation in a comprehensive hospital.

The purpose of this paper is to study the application of advanced computer image processing techniques for flaw detection on flexible printed circuit (FPC) solder.

Texture directionality feature is obtained based on texture gradient, contour's position is extracted and directionality information obtained through analyzing the distribution of directionality. Contour similarity function is established to filter out false contour and keep proper contour, and the solder's location work is accomplished based on reversed contour. After that, a combination of grey and texture gradient's value deviation from reference value is utilized to reflect and describe texture on the solder's surface. Flaw can be distinguished from homogeneous texture background.

The method has been applied to the inspecting system and achieved a higher accuracy and a lower false defect rate. It demonstrates that the method can detect flaws efficiently and effectively.

Although the work on FPC solder's location and flaw detection is presented, defective classification is not involved that is also very important content for inspection.

The paper provides a new way to locate solder based on directionality. The method not only extracts contour feature but also gains directional parameters to help realize accurate location, especially for some solders that are deformed to some extent. Entropy statistic based on distribution of grey and texture gradient is proposed to describe and measure solder's surface texture. The new algorithm performs stably and efficiently and is fit for practical application.

A core challenge of assessing regional agricultural drought vulnerability (RADV) is to reveal what vulnerability factors, under which kinds of synergistic combinations and at what strengths, will lead to higher vulnerability: namely, the influence patterns of RADV.

A two-phased grey rough combined model is proposed to identify influence patterns of RADV from a new perspective of learning and mining historical cases. The grey entropy weight clustering with double base points is proposed to assess degrees of RADV. The simplest decision rules that reflect the complex synergistic relationships between RADV and its influencing factors are extracted using the rough set approach.

The results exemplified by China's Henan Province in the years 2008–2016 show higher degrees of RADV in the north and west regions of the province, in comparison with the south and east. In the patterns with higher RADV, the higher proportion of agricultural population appears in all decision rules as a core feature. A smaller quantity of water resources per unit of cultivated land area and a lower adaptive capacity, involving levels of irrigation technology and economic development, present a significant synergistic influence relationship that distinguishes the features of higher vulnerability from those of the lower.

The proposed grey rough combined model not only evaluates temporal dynamics and spatial differences of RADV but also extracts the decision rules between RADV and its influencing factors. The identified influence patterns inspire managerial implications for preventing and reducing agricultural drought through its historical evolution and formation mechanism.

The purpose of this paper is to establish a combined model for selecting key indexes of complex equipment, and then improve the cost forecasting precision of the model. The problem how to choose the key elements of complex products has always been concerned on many fields, such as cost assessment, investment decision making, etc.

Using Grey System Theory to establish a cost estimation model of complicated equipment is more reasonable under the few data and poor information. Therefore, this paper constructs cost index’s system of complex equipment, and then quantitative and qualitative analysis methods are utilized to calculate the grey entropy between the characteristic parameter and the behavior parameters. Further, establish the grey relational clustering matrix of the behavior sequences by using the grey relative incidence analysis. Finally, the authors select key indicators according to the grey degree.

The experiment demonstrates that the cost key parameters of complex equipment can be successfully screened out by the proposed approach, and the cost estimation accuracy of complicated products is improved.

The method proposed in this paper could be utilized to solve some practical problems, particularly the selection of cost critical parameters for complex products with few samples and poor information. Taking the cost key indexes of civil aircraft as an example, the results verified the validity of the GICM model.

In this paper, the authors develop the method of GICM model. Taking the data of civil aircraft as an example, the authors screen the key indicators of complex products successfully, and improve the prediction accuracy of the GM (1, N) model by using the selected parameters, which provides a reference for some firms.

The purpose of this paper is to propose a dynamic multi-attribute decision-making method based on the prospect theory for dealing with the dynamic multi-attribute decision-making problem with three-parameter interval grey number.

First, the kernel and comparison rule of three-parameter interval grey numbers are defined, which are the basis of collecting and sorting grey numbers. Next, the prospect value function is determined in view of the decision-making information with different time points as the reference points. Then, an optimal model for solving the attribute weight and time weight is constructed based on the grey entropy principle.

The paper provides a dynamic grey interrelation decision method based on the prospect theory with three-parameter interval grey number, and the example analysis shows that the method proposed in this paper has validity and rationality.

If we have a better understanding of the weights of different reference points, it is possible to receive a more reasonable expression for the comprehensive prospect utility value function.

The paper provides a grey interrelation decision method based on the prospect theory, which can help the decision maker deal with the dynamic multi-attribute decision-making problems under the uncertain environment.

The paper proposes the kernel and ranking method of three-parameter interval grey number, and uses different time points as the reference points to define the prospect value function. Furthermore, this paper structures a dynamic grey interrelation decision method with three-parameter interval grey number based on the prospect theory.

The purpose of this paper is to propose the grey target decision method based on three-parameter interval grey number for dealing with multi-attribute decision-making problems under uncertain environment.

First, the kernel and ranking method of three-parameter interval grey number are defined, which is the basis of determining the positive and negative bull’s-eye. Next, a new distance measure of three-parameter interval grey number is defined in view of the importance of the “center of gravity” point. Furthermore, a new comprehensive bull’s-eye distance is proposed based on the kernel which integrates the distance between different attributes to the positive and negative bull’s-eye. Then attribute weights are obtained by comprehensive bull’s-eye distance minimum and grey entropy maximization.

The paper provides a grey target decision method based on three-parameter interval grey number and example analysis shows that the method proposed in this paper is more reasonable and effective.

If we have a better understanding of the distribution characteristics of three-parameter interval grey number, it is possible to have a more reasonable measure of the distance of three-parameter interval grey number.

The paper provides a grey target decision method, which can help decision maker deal with multi-attribute decision-making problems under uncertain environment.

This paper proposed the kernel and ranking method of three-parameter interval grey number, and defined a new distance measure of three-parameter interval grey number and proposed a new comprehensive bull’s-eye distance, Furthermore, this paper structured a grey target decision method based on three-parameter interval grey number.

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.