Grey Systems

Purpose In many instances, the data exhibits periodic and trend characteristics. However, indices like the Digital Economy Development Index (DEDI), which pertains to science, technology, policy and economy, may occasionally display erratic behaviors due to external influences. Thus, to address the unique attributes of the digital economy, this study integrates the principle of information prioritization with nonlinear processing techniques to accurately forecast rapid and anomalous data. Design/methodology/approach The proposed method utilizes the new information priority GM(1,1) model alongside an optimized BP neural network model achieved through the gradient descent technique (GD-BP). Initially, the provincial Digital Economic Development Index (DEDI) is derived using the entropy weight approach. Subsequently, the original GM(1,1) time response equation undergoes alteration of the initial value, and the time parameter is fine-tuned using Particle Swarm Optimization (PSO). Next, the GD-BP model addresses the residual error. Ultimately, the prediction outcome of the grey combination forecasting model (GCFM) is derived by merging the findings from both the NIPGM(1,1) model and the GD-BP approach. Findings Using the DEDI of Jiangsu Province as a case study, researchers demonstrate the effectiveness of the grey combination forecasting model. This model achieves a mean absolute percentage error of 0.33%, outperforming other forecasting methods. Research limitations/implications First of all, due to the limited data access, it is impossible to obtain a more comprehensive dataset related to the DEDI of Jiangsu Province. Secondly, according to the test results of the GCFM from 2011 to 2020 and the forecasting results from 2021 to 2023, it can be seen that the results of the GCFM are consistent with the actual development situation, but it cannot guarantee the correctness of the long-term forecasting, so the combination forecasting model is only suitable for short-term forecasting. Originality/value This article proposes a grey combination prediction model based on the principles of new information priority and nonlinear processing.

Pingping Xiong

Jun Yang

Jinyi Wei

Hui Shu

Grey Systems Theory and Application

Prediction of provincial Digital Economy Development Index based on grey combination forecasting model

基于灰色组合预测模型的省级数字经济发展指数预测

Purpose In this paper, a new grey Cosine New Structured Grey Model (CNSGM(1,N)) prediction power model is constructed for the small-sample modeling and prediction problem with complex nonlinearity and insignificant volatility. Design/methodology/approach Firstly, the weight of some relevant factors is determined by the grey comprehensive correlation degree, and the data are preprocessed. Secondly, according to the principle of “new information priority” and the volatility characteristics of the sequence growth rate, the ideas of damping accumulation power index and trigonometric function are integrated into the New Structured Grey Model (NSGM(1,N)) model. Finally, the non-structural parameters are optimized by the genetic algorithm, and the structural parameters are calculated by the least squares method, so a new CNSGM(1,N) predictive power model is constructed. Findings Under the principle of “new information priority,” through the combination with the genetic algorithm, the traditional first-order accumulation generation is transformed into damping accumulation generation, and the trigonometric function with the idea of integer is introduced to further simulate the phenomenon that the volatility is not obvious in the real system. It is applied to the simulation and prediction of China’s carbon dioxide emissions, and compared with other comparison models; it is found that the model has a better simulation effect and excellent performance. Originality/value The main contribution of this paper is to propose a new grey CNSGM(1,N) prediction power model, which can not only be applied to complex nonlinear cases but also reflect the differences between the old and new data and can reflect the volatility characteristics of the characteristic behavior sequence of the system.

Ye Li

Chengyun Wang

Junjuan Liu

Damped accumulation-based volatility multivariable grey prediction power model and its application

基于阻尼累加的波动性多变量灰色预测电力模型及其应用

Purpose The purpose of the paper is to improve the rating prediction accuracy in recommender systems (RSs) by metric learning (ML) method. The similarity metric of user and item is calculated with gray relational analysis. Design/methodology/approach First, the potential features of users and items are captured by exploiting ML, such that the rating prediction can be performed. In metric space, the user and item positions can be learned by training their embedding vectors. Second, instead of the traditional distance measurements, the gray relational analysis is employed in the evaluation of the position similarity between user and item, because the latter can reduce the impact of data sparsity and further explore the rating data correlation. On the basis of the above improvements, a new rating prediction algorithm is proposed. Experiments are implemented to validate the effectiveness of the algorithm. Findings The novel algorithm is evaluated by the extensive experiments on two real-world datasets. Experimental results demonstrate that the proposed model achieves remarkable performance on the rating prediction task. Practical implications The rating prediction algorithm is adopted to predict the users' preference, and then, it provides personalized recommendations for users. In fact, this method can expand to the field of classification and provide potentials for this domain. Originality/value The algorithm can uncover the finer grained preference by ML. Furthermore, the similarity can be measured using gray relational analysis, which can mitigate the limitation of data sparsity.

Jiangmei Chen

Wende Zhang

Qishan Zhang

Enhancing rating prediction for recommendation by metric learning with gray relational analysis

通过灰色关联分析的度量学习提升推荐系统的评分预测

Purpose The Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers. Design/methodology/approach First, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative. Findings An example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects. Practical implications The proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields. Originality/value The proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

Ruipu Tan

Lehua Yang

Shengqun Chen

Decision-making method based on game theory and grey theory in a single-value neutrosophic environment and its application to typhoon disaster assessment

基于博弈论和灰色理论的单值中智环境决策方法及其在台风灾害评估中的应用

Purpose The purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences. Design/methodology/approach The definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied. Findings The negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility. Practical implications The proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model. Originality/value The definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

Sifeng Liu

Negative grey relational model and measurement of the reverse incentive effect of fields medal

菲尔兹奖逆向激励效应的负灰色关联模型与测量

Purpose The purpose of this paper is to optimize the degradation test for products subject to multiple types of inherent stresses and external random shocks. The mechanism that shows how the variables to be optimized influence the considered multiple objectives is also aimed to be explored by using the grey incidence analysis (GIA) model. Design/methodology/approach The Gamma process is employed to model the influences of different types of stresses and external random shocks. The GIA model is introduced to transfer multiple considered objectives as a comprehensive degree of grey incidence. The particle swarm optimization is integrated to search the globally optimal value of the characteristic variables to be optimized. Findings The acceleration of tested stresses and external random shocks both make the engineering systems become more vulnerable to the inherent degradation. And, the Kriging model can provide guidance of searching the optimal values of test characteristic variables and mitigate the computation burden. The grey incidence model can make the optimization focused and improve the optimality of objective values. Originality/value The proposed method can effectively overcome the drawbacks brought by the limitation of test data and can specify the dependence strength between the inherent degradation and external random shock. The computation cost and accuracy of optimization can be simultaneously ensured by the proposed model.

Weikang Zhang

Huiru Gu

Sainan Wu

Shusen Zhong

Jing Yang

Huiqin Luan

Qi Li

A grey incidence-based algorithm for optimization of accelerated degradation test

基于灰色关联的加速退化试验优化算法

Purpose Traditional grey models are integer order whitening differential models; these models are relatively effective for the prediction of regular raw data, but the prediction error of irregular series or shock series is large, and the prediction effect is not ideal. Design/methodology/approach The new model realizes the dynamic expansion and optimization of the grey Bernoulli model. Meanwhile, it also enhances the variability and self-adaptability of the model structure. And nonlinear parameters are computed by the particle swarm optimization (PSO) algorithm. Findings Establishing a prediction model based on the raw data from the last six years, it is verified that the prediction performance of the new model is far superior to other mainstream grey prediction models, especially for irregular sequences and oscillating sequences. Ultimately, forecasting models are constructed to calculate various energy consumption aspects in Chongqing. The findings of this study offer a valuable reference for the government in shaping energy consumption policies and optimizing the energy structure. Research limitations/implications It is imperative to recognize its inherent limitations. Firstly, the fractional differential order of the model is restricted to 0 &lt; a &lt; 2, encompassing only a three-parameter model. Future investigations could delve into the development of a multi-parameter model applicable when a = 2. Secondly, this paper exclusively focuses on the model itself, neglecting the consideration of raw data preprocessing, such as smoothing operators, buffer operators and background values. Incorporating these factors could significantly enhance the model’s effectiveness, particularly in the context of medium-term or long-term predictions. Practical implications This contribution plays a constructive role in expanding the model repertoire of the grey prediction model. The utilization of the developed model for predicting total energy consumption, coal consumption, natural gas consumption, oil consumption and other energy sources from 2021 to 2022 validates the efficacy and feasibility of the innovative model. Social implications These findings, in turn, provide valuable guidance and decision-making support for both the Chinese Government and the Chongqing Government in optimizing energy structure and formulating effective energy policies. Originality/value This research holds significant importance in enriching the theoretical framework of the grey prediction model. Highlights The highlights of the paper are as follows: A novel grey Bernoulli prediction model is proposed to improve the model’s structure. Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model. The proposed model can achieve full compatibility with the traditional mainstream grey prediction models. Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models. The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

Xiaozeng Xu

Yikun Wu

Bo Zeng

Forecasting short-term energy consumption in Chongqing using a novel grey Bernoulli model

基于新型灰色伯努利模型的重庆短期能源消费预测

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value The model in this paper has supplemented and improved the grey relational analysis theory for panel data.

Aqin Hu

Naiming Xie

Construction and application of a novel grey relational analysis model considering factor coupling relationship

考虑因素耦合关系的新型灰色关联分析模型的构建与应用

Abbreviation	GS
Journal Impact	3.10
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q1)

ISSN	2043-9377, 2043-9385
h-index	30

Publication Information	Publisher: Emerald Group Publishing Ltd.，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2011，Proportion of original research papers: 92.31%，Self Citation Rate:34.40%， Gold OA Rate: 0.99%

Grey Systems

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Prediction of provincial Digital Economy Development Index based on grey combination forecasting model

Damped accumulation-based volatility multivariable grey prediction power model and its application

Enhancing rating prediction for recommendation by metric learning with gray relational analysis

Decision-making method based on game theory and grey theory in a single-value neutrosophic environment and its application to typhoon disaster assessment

Negative grey relational model and measurement of the reverse incentive effect of fields medal

Damped accumulation-based volatility multivariable grey prediction power model and its application

Prediction of provincial Digital Economy Development Index based on grey combination forecasting model

A grey incidence-based algorithm for optimization of accelerated degradation test

Forecasting short-term energy consumption in Chongqing using a novel grey Bernoulli model

Construction and application of a novel grey relational analysis model considering factor coupling relationship