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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.

The goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.

This study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.

We present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.

This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.

The presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

The objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.

This article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.

We showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.

This article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.

The proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

This paper aims to optimize the air pressure regulation scheme of the aeroengine pressure test bench.

Based on the requirements of pressure regulation process and the operating mechanism of aeroengine pressure test bench, a grey performance evaluation index system is constructed. The combination of principal component analysis and grey theory is employed to assign weights to grey indexes. The grey target evaluation model is introduced to evaluate the performance of historical regulation processes, and the evaluation results are analyzed to derive optimization mechanism for pressure regulating schemes.

A case study based on monitoring data from nearly 300 regulation processes verifies the feasibility of the proposed method. On the one hand, the improved principal component analysis method can achieve rational weighting for grey indexes. On the other hand, the method comparison intuitively shows that the proposed method performs better.

The pressure test bench is a fundamental technical equipment in the aviation industry, serving the development and testing of aircraft engines. Due to the complex system composition, the pressure and flow adjustment of the test bench heavily rely on manual experience, leading to issues such as slow adjustment speed and insufficient accuracy. This paper proposes a performance evaluation method for the regulation process of pressure test bench, which can draw knowledge from historical regulation processes, provide guidance for the pressure regulation of test benches, and ultimately achieve the goal of reducing equipment operating costs.

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.

Globally, the landscape of corporate carbon disclosures (CCD) is continually evolving as societal, environmental and regulatory expectations change over time. The goal of this study is to examine the challenges faced by Indian firms’ corporate carbon reporting (CCR). The literature recognized the hurdles to reaching net zero emissions and decarbonization, which are equally applicable to carbon disclosure (CD).

The scope 3 emission disclosure barriers (S3EDBs) identified from the literature were ranked, and their relationships were discovered using the “Grey-based decision-making trial and evaluation laboratory” (Grey- DEMATEL) technique.

The key findings are the S3EDBs, the most prominent barriers, their interrelationships and important insights for managers of organizations in prioritizing the action area for scope 3 CD. Eight S3EDBs were categorized in terms of cause and effect, threshold value is calculated as 0.78. “Quality, and reliability of data,” “Government policies and statutory requirement on emission disclosure” and “Traceability and managing supply chain partners” are the most prominent S3EDBs.

The results will help industry people in countries with emerging economies that have significant scope 3 carbon footprints. The managers can plan to deal with top S3EDBs as a step towards decarbonization and ultimately fighting climate change (CC).

This study is one of the first to rank these barriers to CD so that industry practitioners can prioritize their actions. The core contribution of this research is to detect the most significant S3EDBs and their interdependencies.

This study aims to enhance the assessment of green governance in energy projects along the Belt and Road, reduce the influence of fuzzy judgment, and construct a grey network analysis model from the perspective of Environmental, Social, and Governance (ESG).

The ESG concept is used to establish an evaluation indicator system. The Analytic Network Process (ANP) and the Grey System Theory are applied sequentially to determine the green governance grade of energy projects, exemplified by an evaluation of five projects.

The Karot hydropower project has the best green governance status among the five projects and is of excellent grade. This is followed by the Hongfeng photovoltaic project, the De Aar wind power project, and the Yamal liquefied natural gas project, which are of good grade. The Lamu coal power station project has the worst green governance and is at a medium level.

This study can assist Belt and Road energy projects in identifying their deficiencies and promoting sustainable development by providing a robust framework for green governance evaluation.

The indicator system developed in this study includes social and project governance aspects in addition to environmental performance, reflecting the comprehensive green governance status of projects. The combined use of ANP and grey system theory fully considers the mutual influence relationship between indicators and improves the objectivity of green governance grade judgment.

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.

This study aims to determine the key indicators affecting the resilience of the construction supply chain to flooding and calculate the resilience of the urban construction supply chain in three cases city.

This study combines expert opinions and literature review to determine key indicators and establish a fuzzy EWM-GRA-TOPSIS evaluation model. The index weight was calculated using the entropy weight method, and GRA-TOPSIS was used for comprehensive evaluation.

The results of the study show that the three cities are ranked from the high to low in order of Hangzhou, Hefei and Zhengzhou.

The innovative method adopted in this study comprising EWM-GRA-TOPSIS reduced the influence of subjectivity, fully extracted and utilized data, in a way that respects objective reality. Further, this approach enabled the absolute and relative level of urban construction supply chain resilience to be identified, allowing improvements in the comprehensiveness of decision-making. The method is relatively simple, reasonable, understandable, and computationally efficient. Within the approach, the entropy weight method was used to assign different index weights, and the GRA-TOPSIS was used to rank the resilience of the construction supply chain in three urban cities. The development of resilience provides a robust decision-making basis and theoretical reference, further enriching research methods, and having strong practical value. The study serves to improve risk awareness and resilience, which in turn helps to reduce losses. It also provides enhanced awareness regarding the future enhancement of supply chain resilience for urban construction.

As environmental protection and sustainable development become more widely recognized, greater emphasis has been placed on the significance of green supplier selection (GSS), which can support businesses both upstream and downstream in enhancing their environmental performance while preserving their strategic competitiveness. Therefore, this paper aims to propose a new framework to study GSS.

Firstly, this paper establishes a GSS evaluation criteria system including product competitiveness, green performance, quality of service and enterprise social responsibility. Secondly, based on the spherical fuzzy sets (SFSs), the Average Induction Ordered Weighted Averaging Operator-Criteria Importance Through Inter Criteria Correlation (AIOWA-CRITIC) method is used to determine the subjective and objective weights and the combination of weights are determined by game theory. In addition, the GSS framework is constructed by the Cumulative Prospect Theory-Technique for Order Preference by Similarity to Ideal Solution (CPT-TOPSIS) method. Finally, the validity and robustness of the framework is verified through sensitivity comparative and ablation analysis.

The results show that Y3 is the most promising green supplier in China. This study provides a feasible guidance for GSS, which is important for the greening process of the whole supply chain.

Under spherical fuzzy sets, AIOWA and CRITIC are used to determine weights of indicators. CPT and TOPSIS are combined to construct a decision model, considering the ambiguity and uncertainty of information and the risk attitudes of decision-makers.