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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.

This study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.

In this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.

The results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.

The paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

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.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

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.

The aim of this research was to evaluate the maturity level of strategic communication management implemented by Brazilian startups.

This study employed the analytic hierarchy process (AHP), survey and Grey Fixed Weight Clustering modeling techniques. Three experts with extensive academic and practical experience in the subject participated in the AHP process, providing their opinions on the relative importance of eight variables associated with the topic under investigation, thus enabling their prioritization. Concurrently, data were collected through a survey from 23 respondents who have extensive knowledge about the realities of Brazilian startups. The weights derived from the AHP and the survey data were utilized in the Grey Fixed Weight Clustering modeling.

Based on the opinions of the 23 respondents, the level of implementation of practices related to strategic management, brand management, external image management and internal communication management is superficial. In addition, according to the majority of experts, Brazilian startups exhibited a medium level of maturity to address the key challenges related to communication management. Furthermore, this study reveals that the variables “financial resources allocation,” “stakeholder relationship” and “brand management” were deemed the most significant for the model.

The contributions presented herein can be beneficial for both researchers and startup managers seeking to enhance communication strategies in their organizations. This research also contributes by highlighting how grey systems theory can be extremely useful for conducting decision-making analyses in the context of startups, which is characterized by uncertainty and imprecise information.