Table of Content

01 February 2024, Volume 36 Issue 2

Previous Issue    Next Issue

A Conformable Fractional Non-homogeneous Grey Forecasting Model with Adjustable Parameters CFNGMA(1,1,k,c) and its Application 

Wenqing Wu , Xin Ma , Bo Zeng , Peng Zhang

2024, 36(2):  1-12. 

Asbtract ( 121 )  

Related Articles | Metrics

The inconsistency between the whitening differential equation and the grey basic form of the non-homogeneous continuous grey model CFNGM(1,1,k,c) will result in internal errors. Thus this paper proposes a CFNGMA(1,1,k,c) model with adjustable parameters, which improves the accuracy of the CFNGM(1,1,k,c). This paper first elucidates reasons for the internal errors generated by the continuous grey model CFNGM(1,1,k,c), and explains the classic method, the discrete grey forecasting model, of eliminating internal errors. On the basis of an in-depth analysis of the modeling mechanism of CFNGM(1,1,k,c) model, a new parameter adjustable grey forecasting model is proposed by introducing parameter adjustment factors to modify model’s parameters. Finally, the new model is applied to explore the gross regional product of Chengdu and Deyang in the Chengdu metropolitan area. The calculation results indicate that the newly proposed model can obtain more accurate results. 

Grey Target Decision Extended Model Based on Prospect Theory and Dual Hesitant Fuzzy Set 

Sen Zheng , Lirong Jian, Sifeng Liu, Jie Zhang

2024, 36(2):  13-26. 

Asbtract ( 60 )  

Related Articles | Metrics

Grey target decision-making, as an effective method for multi-attribute decision problems, has been applied to evaluations in various domains. However, existing grey target decision-making method fails to mitigate the inherent subjectivity of decision-makers’ preferences and cannot address the dependency issues in raw data. To address these limitations, this paper proposes an extended model of grey target decision-making based on prospect theory in a dual hesitant fuzzy environment. Firstly, by referencing the positive, negative, and median expected points of each dual hesitant fuzzy decision matrix and employing the prospect theory value function for numerical transformation, a dual hesitant fuzzy prospect matrix is formed. Secondly, utilizing the projection distance and the rewardpenalty principle, the comprehensive target center distance of the decision matrix is calculated to identify the superiority or inferiority of different alternatives. Furthermore, a nonlinear model with minimal comprehensive target center distance is established based on the principle of maximum entropy to optimize attribute weights. Finally, the effectiveness and rationality of the proposed decision-making method are validated through a case study of ecological assessment in the aviation industry cluster.  

GN.Gompertz Model under Information Progressive Coverage for Reliability Growth Based on Complex Equipment Collaborative Network  

Yangyang Du , Yadong Zhang, Sifeng Liu , Zhigeng Fang

2024, 36(2):  27-36. 

Asbtract ( 49 )  

Related Articles | Metrics

The development of complex equipment has the feature of "main manufacturer-supplier", with a large amount of underlying data and a small amount of top-level data for reliability growth. This paper firstly introduces the basic model of reliability growth. For small samples and uncertain of complex equipment, Bayesian methods and grey system theory have also been investigated. It has been found that existing research cannot describe this distributed collaborative network and the inherent mechanism of reliability growth, and the information data of reliability growth had not been fully utilized. This paper proposes a new model that combines Bayesian and GERT networks. This model is suitable for evaluating the reliability growth process in collaborative development networks, and can make full use of supplier information, historical information, and experimental information to comprehensively evaluate the reliability growth. Through case analysis of the flight control system, it is proven that the new model performs well in comprehensively utilizing various types of information.  

Forecasting PM_2.5 Concentration with a Novel Seasonal Discrete Multivariable Grey Model Incorporating Spatial Influencing Factors 

Yuanping Ding, Yaoguo Dang, Junjie Wang, Qingyuan Xue

2024, 36(2):  37-53. 

Asbtract ( 80 )  

Related Articles | Metrics

Given that PM2.5 concentration is not only related to local pollutants, but also affected by long-distance transmission of PM2.5 in adjacent areas, the key to improving the prediction accuracy of PM2.5 concentration is to comprehensively consider the effect of local influencing factors and the transmission effect of PM2.5 in adjacent areas. For this purpose, a novel seasonal discrete multivariable grey prediction model, encompassing spatial influencing factors, has been established. Firstly, we analyze the mechanism of spatial influencing factors and the reasonableness of using PM2.5 concentration in adjacent areas as the spatial influencing factors. Secondly, based on the spatial agglomeration characteristics of PM2.5 concentration, the K − means clustering algorithm is used to cluster adjacent cities with similar PM2.5 concentration, then the comprehensive value of PM2.5 concentration in each city cluster is calculated by weighted average combination. On this basis, a driving term of spatial influencing factors and a cosine trigonometric function term are introduced into the novel model to characterize the effect of spatial influencing factors on PM2.5 concentration and the seasonal fluctuation of itself, respectively. More importantly, the Genetic Algorithm Toolbox is employed to optimally determine the emerging parameters of this model, and the time response function of the novel model is calculated by mathematical induction method. Lastly, the new model is deemed valid through testing its PM2.5 concentration predictions for the cities of Beijing, Tianjin, and Baoding in the Beijing-TianjinHebei region. Based on the original observations from 2018Q1 to 2023Q2, the novel model is built for PM2.5 concentration prediction in 2023Q3 to 2024Q2 for the three cities. The findings imply that the newly developed model outperforms its competitors significantly and has the potential to serve as a robust tool for predicting PM2.5 concentration.

Reinforcement Model for Unmanned Combat System of Systems Based on Multi-Layer Grey Target 

Xueting Hao, Zhigeng Fang, Jingru Zhang, Fei Deng, Ankang Jiang, Shuyu Xiao

2024, 36(2):  54-66. 

Asbtract ( 71 )  

Related Articles | Metrics

In the future battlefield, unmanned combat mode will be crucial. Its attack strategy formulation is a significant and complex task. To address the issue of decisionmaking in unmanned combat system of systems(UCSoS) striking strategy, this paper begins by analyzing the characteristics of UCSoS. By utilizing the GERT concept, an unmanned combat A-GERT network is developed to provide parameter support for evaluating its effectiveness. Secondly, for effectiveness evaluation, a multi-layer gray target model built on the A-GERT network is proposed. This model is utilized to formulate the optimal striking scheme for the UCSoS. And Agent technology is employed to solve the intelligent learning decision-making problem for UCSoS based on multi-layer grey target model. Finally, a case study illustrates the efficiency and effectiveness of the reinforcement model for UCSoS based on multi-layer grey target.

An Optimized Multivariate Grey Bernoulli Model for Forecasting Fossil Energy Consumption in China  

Ye Li , Dongyu Liu, Meidan Xiao, Bin Liu

2024, 36(2):  67-78. 

Asbtract ( 117 )  

Related Articles | Metrics

Given the increasing severity of energy shortages, the exploration of effective strategies to optimize energy structures has become imperative. This requires careful consideration of energy consumption patterns, especially since these data are fundamental inputs for policy formulation. Given the uncertainty in the rate of change in energy consumption, this paper proposes an optimized multivariable grey Bernoulli model that is rooted in the grey Bernoulli model and incorporates background values and genetic algorithms. The grey Bernoulli model effectively linearizes nonlinear problems, thus simplifying computational procedures. In addition, to account for random fluctuations of relevant factors that may affect the model's predictions, this model introduces nonlinear correction terms that allow simulation and prediction values to adhere to the grey index law. The incorporation of background values enhances the model's ability to process information, providing it with a superior grasp of real data. Genetic algorithms can be used to refine the model's parameters, increasing its adaptability and precision. Finally, this paper applies the refined model to examine China's energy consumption patterns, validating its efficacy and versatility. Furthermore, energy consumption patterns for the next four years are forecast, with the analysis revealing that the growth rate of energy consumption from 2021 to 2024 shows a downward trend, particularly notable in 2024, where the growth rate is 1.64%. 

Parameter Estimation of Integro-differential Equation-based Grey Predator-prey Model From Noisy Data 

Zhaoya Zhang, Naiming Xie, Lu Yang, Xiaolei Wang

2024, 36(2):  79-89. 

Asbtract ( 62 )  

Related Articles | Metrics

The grey predator-prey model is widely applied in many fields for its effectiveness. While most of the research on the grey predator-prey model focuses on the different model forms, less attention has been paid to identifying parameters and initial value from noisy data. In this work, considering the measurement noise in practice, we propose a two-stage approach to estimate the structural parameters and initial value of the grey predator-prey model with integro-differential equations(IDEs). First, by introducing an integral operator, we propose another form of the grey predator-prey model, namely the IDE-based grey predator-prey model. Next, we develop a parameter estimation approach based on the idea of a two-stage in the presence of measurement noise, where in the first stage we smooth time series using cubic B-Spline and in the second stage estimate structural parameters and initial conditions by the separable nonlinear least squares. Then, the finite sample performance of the IDE-based model is investigated with Monte Carlo numerical experiments. Results demonstrate that the IDE-based model has better performance in terms of accuracy than the Cusum-based model. Finally, we use a case to further verify the accuracy and stability of the proposed method.  

Discovering the mechanism of grey forecasting models from the perspective of dynamic system modelling  

Xiaolei Wang, Naiming Xie

2024, 36(2):  90-99. 

Asbtract ( 65 )  

Related Articles | Metrics

Grey forecasting models have found extensive applications across various domains, but the connection between their theory and practice has not yet been fully revealed. This paper seeks to discuss the modelling mechanism of grey forecasting models from the perspective of dynamic system modelling and illustrate how to establish grey forecasting models to address real-world challenges. Firstly, we outline the grey forecasting models under the traditional and direct frameworks. Then, the problem description and model assumptions of grey forecasting models are discussed by incorporating model characteristics and Prof. Deng's original concepts. The complete process of model establishment as well as the purpose and tasks of each step is elaborated in detail. Ultimately, taking the inventory of perishable products as a case study, this article discusses the utilization of grey forecasting models in inventory management and elucidates the application process using citrus as a specific example.