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The purpose of this paper is to explore a new grey relational analysis model to measure the coupling relationship between the indicators for the water environment status assessment. Meanwhile, the model deals with the problem that the changing of indicator order may result in the changing of the degree of grey relation.

The binary index submatrix of the sample matrix is given first. Then the product of the matrix and its own transpose is used to measure the characteristics of the index and the coupling relationship between the indicators. Thirdly, the grey relational coefficient is defined based on the matrix norm, and a grey coupling relational analysis model is proposed.

The paper provides a novel grey relational analysis model based on the norm of matrix. The properties, normalization, symmetry, relational order invariance to the multiplicative, are studied. The paper also shows that the model performs very well on the water environment status assessment in the eight cities along the Yangtze River.

The model in this paper has supplemented and improved the grey relational analysis theory for panel data.

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.

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.

This paper addresses the challenges associated with forecasting electricity consumption using limited data without making prior assumptions on normality. The study aims to enhance the predictive performance of grey models by proposing a novel grey multivariate convolution model incorporating residual modification and residual genetic programming sign estimation.

The research begins by constructing a novel grey multivariate convolution model and demonstrates the utilization of genetic programming to enhance prediction accuracy by exploiting the signs of forecast residuals. Various statistical criteria are employed to assess the predictive performance of the proposed model. The validation process involves applying the model to real datasets spanning from 2001 to 2019 for forecasting annual electricity consumption in Cameroon.

The novel hybrid model outperforms both grey and non-grey models in forecasting annual electricity consumption. The model's performance is evaluated using MAE, MSD, RMSE, and R², yielding values of 0.014, 101.01, 10.05, and 99% respectively. Results from validation cases and real-world scenarios demonstrate the feasibility and effectiveness of the proposed model. The combination of genetic programming and grey convolution model offers a significant improvement over competing models. Notably, the dynamic adaptability of genetic programming enhances the model's accuracy by mimicking expert systems' knowledge and decision-making, allowing for the identification of subtle changes in electricity demand patterns.

This paper introduces a novel grey multivariate convolution model that incorporates residual modification and genetic programming sign estimation. The application of genetic programming to enhance prediction accuracy by leveraging forecast residuals represents a unique approach. The study showcases the superiority of the proposed model over existing grey and non-grey models, emphasizing its adaptability and expert-like ability to learn and refine forecasting rules dynamically. The potential extension of the model to other forecasting fields is also highlighted, indicating its versatility and applicability beyond electricity consumption prediction in Cameroon.

For some years now, Cameroon has seen a significant increase in its electricity demand, and this need is bound to grow within the next few years owing to the current economic growth and the ambitious projects underway. Therefore, one of the state's priorities is the mastery of electricity demand. In order to get there, it would be helpful to have reliable forecasting tools. This study proposes a novel version of the discrete grey multivariate convolution model (ODGMC(1,N)).

Specifically, a linear corrective term is added to its structure, parameterisation is done in a way that is consistent to the modelling procedure and the cumulated forecasting function of ODGMC(1,N) is obtained through an iterative technique.

Results show that ODGMC(1,N) is more stable and can extract the relationships between the system's input variables. To demonstrate and validate the superiority of ODGMC(1,N), a practical example drawn from the projection of electricity demand in Cameroon till 2030 is used. The findings reveal that the proposed model has a higher prediction precision, with 1.74% mean absolute percentage error and 132.16 root mean square error.

These interesting results are due to (1) the stability of ODGMC(1,N) resulting from a good adequacy between parameters estimation and their implementation, (2) the addition of a term that takes into account the linear impact of time t on the model's performance and (3) the removal of irrelevant information from input data by wavelet transform filtration. Thus, the suggested ODGMC is a robust predictive and monitoring tool for tracking the evolution of electricity needs.

The purpose of this paper is to propose a scenario-based grey methodology using clustering and optimizing with imprecise and uncertain body size data in an emergency assembly point area to assign the people on a campus to reach the emergency assembly points under uncertain disaster times.

Grey clustering and a new grey p-median linear programming model are developed to determine which units to assign to the pre-determined assembly points for a main campus in case of a disaster. The models have two scenarios: 70 and 100% occurrence capacities of administrative and academic personnel and students.

In this study, the academic and administrative units have been assigned to determine five different emergency assembly points on the main campus by using the numbers of the academic and administrative personnel and student and distances of the units to the assembly point areas of each other. The alternative solutions are obtained effectively by evaluating capacity utilization rates in the scenarios.

It is often unclear when disasters can occur and therefore, a preliminary preparation time must be required to minimize the risk. In the case of natural, man-made (unnatural) or technological disasters, the people are required to defend themselves and move away from the disaster area as soon as possible in a proper direction. The proposed assignment model yields a final solution that effectively eliminates uncertainty regarding the selection of emergency assembly points for administrative and academic staff as well as students, in the event of disasters.

Grey clustering suggests an assignment plan and concurrently, an investigation is underway utilizing the grey p-median linear programming model. This investigation aims to optimize various scenarios and body sizes concerning emergency assembly areas. All campus users who are present at the disaster in units of the campus are getting uncertainty about which emergency assembly point to use, and with this study, the vital risks aim to be ultimately reduced with reasonable plans.

The purpose of this paper is to construct a grey incidence model for panel data that can reflect the incidence direction and degree between indicators.

Firstly, this paper introduces the concept of a negative matrix and preprocesses the data of each indicator matrix to eliminate differences in dimensions and magnitudes between indicators. Then a model is constructed to measure the incidence direction and degree between indicators, and the properties of the model are studied. Finally, the model is applied to a practical problem.

The grey-directed incidence degree is 1 if and only if corresponding elements between the feature indicator matrix and the factor indicator matrix have a positive linear relationship. This degree is −1 if and only if corresponding elements between the feature indicator matrix and the factor indicator matrix have a negative linear relationship.

The example shows the number of days with good air quality is negatively correlated with the annual average concentration of each pollutant index. PM_2.5, PM₁₀ and O₃ are the main pollutants affecting air quality in northern Henan.

This paper introduces the negative matrix and constructs a model from the holistic perspective to measure the incidence direction and level between indicators. This model can effectively measure the incidence between the feature indicator and factor indicator by integrating information from the point, row, column and matrix.

Talent is a key resource for urban development, and building and disseminating urban brands have an important impact on attracting talent. This paper explores what kind of urban brand ecology (UBE) can effectively enhance urban talent attraction (UTA). We explore this question using a novel grey quantitative configuration analysis (GQCA) model.

To develop the GQCA model, grey clustering is combined with qualitative configuration analysis (QCA). We conducted comparative configuration analysis of UTA using fuzzy set QCA (fsQCA) and the proposed GQCA.

We find that the empirical results of fsQCA may contradict the facts, and that the proposed GQCA effectively solves this problem.

Based on the theory of UBE, we identify bottleneck factors for improving UTA at different stages. Seven configuration paths are described for cities to enhance UTA. Theoretically, this study expands the application boundaries of UBE.

The proposed GQCA effectively solves the problem of inconsistent analysis and facts caused by the use of a binary threshold by the fsQCA. In practical case studies, the GQCA significantly improves the reliability of configuration comparisons and the sensitivity of QCA to cases, demonstrating excellent research performance.

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.

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.