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Aim to the limitations of grey relational analysis of interval grey number, based on the generalized greyness of interval grey number, this paper tries to construct a grey angle cosine relational degree model from the perspective of proximity and similarity.

Firstly, the algorithms of the generalized greyness of interval grey number and interval grey number vector are given, and its properties are analyzed. Then, based on the grey relational theory, the grey angle cosine relational model is proposed based on the generalized greyness of interval grey number, and the relationship between the classical cosine similarity model and the grey angle cosine relational model is analyzed. Finally, the validity of the model in this paper is illustrated by the calculation examples and an application example of related factor analysis of maize yield.

The results show that the grey angle cosine relational degree model has strict theoretical basis, convenient calculation and is easy to program, which can not only fully utilize the information of interval grey numbers but also overcome the shortcomings of greyness relational degree model. The grey angle cosine relational degree is an extended form of cosine similarity degree of real numbers. The calculation examples and the related factor analysis of maize yield show that the model proposed in this paper is feasible and valid.

The research results not only further enrich the grey system theory and method but also provide a basis for the grey relational analysis of the sequences in which the interval grey numbers coexist with the real numbers.

The paper succeeds in realizing the algorithms of the generalized greyness of interval grey number and interval grey number vector, and the grey angle cosine relational degree, which provide a new method for grey relational analysis.

Assembly line is a common production form and has been effectively used in many industries, but the imprecise processing time of each process makes production line balancing and capacity forecasting the most troublesome problems for production managers. In this paper, uncertain man-hours are represented as interval grey numbers, and the optimization problem of production line balance in the case of interval grey man-hours is studied to better evaluate the production line capacity.

First, this paper constructs the basic model of assembly line balance optimization for the single-product scenario, and on this basis constructs an assembly line balance optimization model under the multi-product scenario with the objective function of maximizing the weighted greyscale production line balance rate, second, this paper designs a simulated annealing algorithm to solve problem. A neighborhood search strategy is proposed, based on assembly line balance optimization, an assembly line capacity evaluation method with interval grey man-hour characteristics is designed.

This paper provides a production line balance optimization scheme with uncertain processing time for multi-product scenarios and designs a capacity evaluation method to provide managers with scientific management strategies so that decision-makers can scientifically solve the problems that the company's design production line is quite different from the actual production situation.

There are few literary studies on combining interval grey number with assembly line balance optimization. Therefore, this paper makes an important contribution in this regard.

In order to explore a new estimation approach of hyperspectral estimation, this paper aims to establish a hyperspectral estimation model of soil organic matter content with the principal gradient grey information based on the grey information theory.

Firstly, the estimation factors are selected by transforming the spectral data. The eigenvalue matrix of the modelling samples is converted into grey information matrix by using the method of increasing information and taking large, and the principal gradient grey information of modelling samples is calculated by using the method of pro-information interpolation and straight-line interpolation, respectively, and the hyperspectral estimation model of soil organic matter content is established. Then, the positive and inverse grey relational degree are used to identify the principal gradient information quantity of the test samples corresponding to the known patterns, and the cubic polynomial method is used to optimize the principal gradient information quantity for improving estimation accuracy. Finally, the established model is used to estimate the soil organic matter content of Zhangqiu and Jiyang District of Jinan City, Shandong Province.

The results show that the model has the higher estimation accuracy, among the average relative error of 23 test samples is 5.7524%, and the determination coefficient is 0.9002. Compared with the commonly used methods such as multiple linear regression, support vector machine and BP neural network, the hyperspectral estimation accuracy of soil organic matter content is significantly improved. The application example shows that the estimation model proposed in this paper is feasible and effective.

The estimation model in this paper not only fully excavates and utilizes the internal grey information of known samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a new hyperspectral estimation model of soil organic matter content based on the principal gradient grey information and effectively dealing with the randomness and grey uncertainty in spectral estimation.

Supplier selection along with continuous evaluation of their performance is a crucial activity in healthcare supply chain management for effective utilization of scarce resources while providing quality service at an affordable price, and minimizing chances of stock-out, avoiding serious consequences on the illness or fatality of the patients. Presence of both qualitative and quantitative evaluation criteria, set of potential suppliers and participation of different stakeholders with varying interest make healthcare supplier selection a challenging task which can be effectively solved using any of the multi-criteria decision making (MCDM) methods.

To deal with various qualitative criteria, like cost, quality, delivery performance, reliability, responsiveness and flexibility, this paper proposes integration of grey system theory with a newly developed MCDM tool, i.e. mixed aggregation by comprehensive normalization technique (MACONT) to identify the best performing supplier for pharmaceutical items in a healthcare unit from a pool of six competing alternatives based on the opinions of three healthcare professionals.

While assessing importance of the six evaluation criteria and performance of the alternative healthcare suppliers against those criteria using grey numbers, and exploring use of three normalization procedures and two aggregation operations of MACONT method, this integrated approach singles out S5 as the most compromised healthcare supplier for the considered problem. A sensitivity analysis of its ranking performance against varying values of both balance parameters and preference parameters also validates its solution accuracy and robustness.

This integrated approach can thus efficiently solve healthcare supplier selection problems based on qualitative evaluation criteria in uncertain group decision making environment. It can also be deployed to deal with other decision making problems in the healthcare sector, like supplier selection for healthcare devices, performance evaluation of healthcare units, ranking of physicians etc.

The purpose of this paper is to explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

This paper sets out to solve a common and crucial fundamental theoretical problem of gray incidence cluster analysis: to [X]={X|ρ(X,Y)≥1−ε0} constitute an approximate classification, it must first be proven that [X]={X|ρ(X,Y)=1} constitutes a rigorous classification.

This paper does not study the concrete expressions of various incidence degrees but rather the perfect correlation essence of such incidence degrees, that is, sufficient and necessary conditions.

For any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree, it is proven that the perfect correlation relation is an equivalence relation. The set composed of all sequences Y that are equivalent to sequences X is studied, that is, the equivalence class of X. The structure and mutual relations of these equivalence classes are discussed, and the topological homeomorphism concept of incidence degree is introduced. The conclusion is obtained that the equivalence classes of the two incidence degrees must be the same when the topological homeomorphism is obtained.

In this paper, only the perfect correlation relation of any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree are studied as equivalent relations.

Not only are the research results of several incidence degrees involved in this paper original but also many other effective incidence degrees have not done this basic research, so this paper opens up a research direction with theoretical significance.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

The purpose of this study is to advance a novel evaluation index system and evaluation approach for ability of older adults in China.

This study constructed a comprehensive older adult ability evaluation index system with 4 primary indicators and 17 secondary indicators. Grey clustering analysis and entropy weight method are combined into a robust evaluation model for the ability of older adults.

The result demonstrates that the proposed grey clustering model is readily available to calculate the disability level of elderly individuals. The constructed index system more comprehensively considers all aspects of the disability of the elderly.

This study provides a quantitative method and a more reasonable index system for the determination of the disability level of the elderly.

The purpose of this study is to establish a grey-entropy-catastrophe progression method (CPM) model to assess the photovoltaic (PV) industry chain resilience of Jiangsu Province in China.

First, we designed the resilience evaluation index system of such a chain from two aspects: the external environment and internal conditions. We then constructed a PV industry chain resilience evaluation model based on the grey-entropy-CPM. Finally, the feasibility and applicability of the proposed model were verified via an empirical case study analysis of Jiangsu Province in China.

As of the end of 2022, the resilience level of its PV industry chain is medium-high resilience, which indicates a high degree of adaptability to the current unpredictable and competitive market, and can respond to the uncertain impact of changes in conditions effectively and in a timely manner.

The construction of this model can provide reference ideas for related enterprises in the PV industry to analyze the resilience level of the industrial chain and solve the problem of industrial chain resilience.

Firstly, an analysis of the entire industrial chain structure of the PV industry, combined with its unique characteristics is needed to design a PV industry chain resilience evaluation index system. Second, grey relational analysis (GRA) and the entropy method were adopted to improve the importance of ranking the indicators in the evaluation of the CPM, and a resilience evaluation model based on grey-entropy-CPM was constructed.

No study has investigated the effects of different parameters on publication bias in meta-analyses using a machine learning approach. Therefore, this study aims to evaluate the impact of various factors on publication bias in meta-analyses.

An electronic questionnaire was created according to some factors extracted from the Cochrane Handbook and AMSTAR-2 tool to identify factors affecting publication bias. Twelve experts were consulted to determine their opinion on the importance of each factor. Each component was evaluated based on its content validity ratio (CVR). In total, 616 meta-analyses comprising 1893 outcomes from PubMed that assessed the presence of publication bias in their reported outcomes were randomly selected to extract their data. The multilayer perceptron (MLP) technique was used in IBM SPSS Modeler 18.0 to construct a prediction model. 70, 15 and 15% of the data were used for the model's training, testing and validation partitions.

There was a publication bias in 968 (51.14%) outcomes. The established model had an accuracy rate of 86.1%, and all pre-selected nine variables were included in the model. The results showed that the number of databases searched was the most important predictive variable (0.26), followed by the number of searches in the grey literature (0.24), search in Medline (0.17) and advanced search with numerous operators (0.13).

The results of this study can help clinical researchers minimize publication bias in their studies, leading to improved evidence-based medicine.

To the best of the author’s knowledge, this is the first study to model publication bias using machine learning.