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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.

In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.

Firstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.

The results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.

The decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.

The paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.

As some data to evaluate the efficiency of bank branches is qualitative or uncertain, only grey numbers should be used to calculate the efficiency interval. The combination of multi-stage models and grey data can lead to a more accurate and realistic evaluation to assess the performance of bank branches. This study aims to compute the efficiency of each branch of the bank as a grey number and to group all branches into four grey efficiency areas.

The key performance indicators are identified based on the balanced scorecard and previous research studies. They are included in the two-stage grey data envelopment analysis (DEA) model. The model is run using the GAMS program. The grey efficiencies are calculated and bank branches have been grouped based on efficiency kernel number and efficiency greyness degree.

As policies and management approaches for branches with less uncertainty in efficiency are different from branches with more uncertainty, considering the uncertainty of efficiency values of branches may be helpful for the policy-making of managers. The grey efficiency of branches of one bank is examined in this study using the two-stage grey DEA throughout one year. The branches are grouped based on kernel and greyness value of efficiency, and the findings show that considering the uncertainty of data makes the results more consistent with the real situation.

The performance of bank branches is modeled as a two-stage grey DEA, in which the efficiency value of each branch is obtained as a grey number. The main originality of this paper is to group the bank branches based on two grey indexes named “kernel number” and “greyness degree” of grey efficiency value.

To overcome the limitations of traditional multi-attribute decision making (MADM) methods, which only provide deterministic rankings of decision objects, this paper proposes a novel multi-attribute 3WD model. This model presents three-parameter interval grey number decision-theoretic rough sets (TPIGNDTRSs), aiming to offer a reasoned interpretation of loss functions in grey environments and ensure objective assessment of conditional probabilities.

Firstly, the traditional equivalence relation is replaced with the probabilistic dominance relation (PDR), categorizing decision objects into two state sets in DTRS for more objective conditional probabilities. Secondly, as the three-parameter interval grey number (TPIGN) introduces the most probable value on the basis of the traditional two-parameter interval grey number, it provides a more comprehensive method for describing grey information. Consequently, integrating TPIGN into DTRS refines the interpretations of loss functions in grey environments. Finally, by utilizing two main sorting techniques, relative kernel and degree of accuracy ranking and possibility ranking, two types of 3WD rules with TPIGNDTRSs, are constructed.

This study has successfully developed and validated a new multi-attribute 3WD model. The model was tested in two distinct domains: evaluating innovation efficiency in high-tech enterprises and recommending movies in a practical case. The findings reveal that the model can effectively integrate relevant information of high-tech enterprises, provide the government with enterprise-level assessments, and gather consumer preferences to recommend the most suitable movies.

This study treats the loss function as grey information in the 3WD model but overlooks the grey nature of evaluation values, limiting its applicability. Additionally, the model’s reliance on subjective expert judgments and historical data to establish the loss function may affect its objectivity. The implications of this research are that the novel model overcomes traditional MADM limitations, enhancing decision-making quality and efficiency in complex and grey scenarios. The model’s successful application in evaluating high-tech enterprises and recommending movies illustrates its dual value in both theory and practice.

Initially, the model proposed in this study is of significant importance for the development of the 3WD field, as it successfully addresses the challenges of uncertain loss functions and unknown conditional probabilities in grey information environments. Moreover, by integrating the 3WD model with MADM problems, it has broken through the bottlenecks of traditional MADM methods, offering new perspectives and strategies for solving MADM issues. Therefore, this research not only advances theoretical research but also provides powerful tools for practical applications.

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?”

Considering the bounded confidence of decision-makers (DMs), a new grey multi-criteria group consensus decision-making (GMCGCDM) model is established by using interval grey number (IGN), cobweb model, social network analysis (SNA) and consensus reaching process (CPR).

Firstly, the model analyzes the social relationship of DM under social networks and proposes a calculation method for DMs’ weights based on SNA. Secondly, the model defines a cobweb model to consider the preferences of decision-making alternatives in the decision-making process. The consensus degree is calculated by the area surrounded by the connections between each index value of DMs and the group. Then, the model coordinates the different opinions of various DMs to reduce the degree of bias of each DM and designs a consensus feedback mechanism based on bounded confidence to guide DMs to reach consensus.

The advantage of the proposed method is to highlight the practical application, taking the selection of low-carbon suppliers in the context of dual carbon as an example. Comparison analysis is performed to reveal the interpretability and applicability of the method.

The main contribution of this paper is to propose a new GMCGCDM model, which can not only expand the calculation method of DM’s weight and consensus degree but also reduce the time and cost of decision-making.

This paper applies fuzzy grey cognitive maps (FGCM) to support multicriteria group decision making (GDM) on supply chain performance (SCP) considering the role of organizational culture as a moderating factor.

This paper follows the quantitative axiomatic prescriptive model-based research. It introduces a MGDM model that relies on the SCOR® model performance attributes and Hofstede’s cultural dimensions. The proposal is underpinned by the soft computing technique of FGCM, aimed at addressing the inherent subjectivity associated with evaluating the culture-performance relationship within supply chains.

The FGCM-based model proposes a management matrix tool for supporting SPC management. It results in a graphical representation that deconstructs SCP and organizational culture into key elements and provides directives for action plans that align improvement efforts. An illustrative application is presented to guide and promote the model’s application in different configurations of supply chains.

This model offers valuable insights into addressing the impact of organizational culture on decision-making related to SCP. Additionally, it facilitates scenario simulation. The management matrix visually illustrates how each performance attribute is influenced by each cultural dimension on a quantitative scale. It also ranks these attributes based on the overall level of influence they receive from culture.

The study provides a unique outlook on the use of FGCMs to support the SCP decisional process by detailing and accounting for the influence of organizational culture. This is done through the development of a novel matrix that allows for visual management and benchmarking.

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.