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Axioms
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Fractional-Order Grey Models and Their Applications
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Fractional-Order Grey Models and Their Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 7830

Special Issue Editor

Prof. Dr. Lifeng Wu

E-Mail Website
Guest Editor
College of Management Engineering and Business, Hebei University of Engineering, Handan 056038, China
Interests: fractional models; grey system model
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus, fractional-order ideal, and fractional operators (the fractional-order model) have gained importance and popularity due to applications in many fields. The grey system model is a hot topic in the management system. It can depict the uncertain information of management systems. The fractional-order grey models have also been extensively studied in recent years. However, we are still at the beginning of applying this very powerful tool in management science. The integral-order grey models are ideal memory models, which are not suitable for describing irregular phenomena. The fractional-order characteristic enables the proposed model to simultaneously exhibit both short- and long-range dependence. The use of fractional order can improve and generalize well-established mathematics methods and strategies. Many different fractional-order schemes are presented for the management system. Fractional-order grey models with power-law memory have shown that memory effects can play an important role in economic phenomena and processes. The fractional-order inventory model has memory effects. The aim of this Special Issue is to investigate the fractional model extent and its applications, with particular emphasis on management system. We invite authors to submit their original research and review articles exploring the issues and extent of the fractional-order grey model.

Prof. Dr. Lifeng Wu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional-order operator and complex number order operator extent
  • grey forecasting model with fractional-order operator
  • fractional auto-regressive integrated moving average model
  • fractional derivative model and fractional integral inequality extent
  • fractional differentiation model and special function extent
  • grey neural network with fractional-order operator
  • fractional-order cuckoo search and other intelligent optimization algorithms
  • fractional-order grey system model and fractional-order uncertain model
  • fractional-order grey inventory model
  • grey support vector machine with fractional-order operator
  • fractional-order ideals in data envelopment analysis and other evaluated models
  • potential and current applications of the fractional-order model

Published Papers (5 papers)

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Research

16 pages, 528 KiB  
Article
Local Grey Predictor Based on Cubic Polynomial Realization for Market Clearing Price Prediction
by Akash Saxena, Adel Fahad Alrasheedi, Khalid Abdulaziz Alnowibet, Ahmad M. Alshamrani, Shalini Shekhawat and Ali Wagdy Mohamed
Axioms 2022, 11(11), 627; https://doi.org/10.3390/axioms11110627 - 08 Nov 2022
Cited by 2 | Viewed by 970
Abstract
With the development of restructured power markets, the profit-making competitive business environment has emerged. With the help of different advanced technologies, generating companies are taking decisions regarding trading electricity with imperfect information about marketing operating conditions. The forecasting of the market clearing price [...] Read more.
With the development of restructured power markets, the profit-making competitive business environment has emerged. With the help of different advanced technologies, generating companies are taking decisions regarding trading electricity with imperfect information about marketing operating conditions. The forecasting of the market clearing price (MCP) is a potential issue in these markets. Early information on the MCP can be a proven beneficial tool for accumulating profit. In this work, a local grey prediction model based on a cubic polynomial function is presented to estimate the MCP with the help of historical data. The mathematical framework of this grey model was established and evaluated for different market conditions and databases. The comparison between traditional grey models and some advanced grey models reveals that the proposed model yields accurate results. Full article
(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)
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10 pages, 779 KiB  
Article
Prediction of the Share of Solar Power in China Based on FGM (1,1) Model
by Yuhan Li, Shuya Wang, Wei Dai and Liusan Wu
Axioms 2022, 11(11), 581; https://doi.org/10.3390/axioms11110581 - 22 Oct 2022
Cited by 3 | Viewed by 1237
Abstract
In recent years, fossil energy reserves have decreased year by year, and the development and use of renewable energy has attracted great attention of governments all over the world. China continues to promote the high-quality development of renewable energy such as solar power [...] Read more.
In recent years, fossil energy reserves have decreased year by year, and the development and use of renewable energy has attracted great attention of governments all over the world. China continues to promote the high-quality development of renewable energy such as solar power generation. Accurate prediction of the share of solar power in China is beneficial to implementing the goals of carbon peaking and carbon neutralization. According to the website of China’s National Bureau of statistics, the earliest annual data of China’s solar power generation is 2017, which leads to there being very few data on the share of China’s solar power generation. Therefore, the prediction accuracy of most prediction methods is low, and the advantages of the grey prediction model are shown. Based on the share of solar power in China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r using the Particle Swarm Optimization (PSO) algorithm, and predicts the share of solar power in China in the next few years. r = 0.3858 and MAPE = 0.20% were obtained by calculation of the model. The prediction results show that the share of solar power generation in China will increase year by year, and it will reach about 4.2301% by 2030. In addition, it is found that the share of China’s solar power generation in 2021 is 2.1520%, and the predicted value is 2.1906%. It can be seen that the prediction error is small. Finally, the limitations and future research directions are elucidated. The prediction results presented in this paper will help to guide the development of solar power generation in China, and are of great significance in speeding up the pace of energy structural adjustment, accelerating the construction of a clean, low-carbon, safe and efficient energy system, and promoting sustainable development. Full article
(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)
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8 pages, 858 KiB  
Article
Prediction of the Total Output Value of China’s Construction Industry Based on FGM (1,1) Model
by Xiao Zhang, Jingyi Wang, Liusan Wu, Ming Cheng and Dongqing Zhang
Axioms 2022, 11(9), 450; https://doi.org/10.3390/axioms11090450 - 02 Sep 2022
Cited by 4 | Viewed by 1191
Abstract
The total output value of the construction industry (TOVCI) reflects its own development level to a certain extent. An accurate prediction of the construction industry’s total output value is beneficial to the government’s dynamic regulation. The grey prediction model is widely used for [...] Read more.
The total output value of the construction industry (TOVCI) reflects its own development level to a certain extent. An accurate prediction of the construction industry’s total output value is beneficial to the government’s dynamic regulation. The grey prediction model is widely used for its simple calculation process and high prediction accuracy. Based on the TOVCI of China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r by a simulated annealing algorithm, and forecasts the TOVCI of China in next few years. At present, the Particle Swarm Optimization algorithm (PSO) is employed in the calculation of r in the literature. However, the advantage of the simulated annealing algorithm is its powerful global search performance. The prediction results indicate that the TOVCI of China will continue to grow, but the growth rate will slow down. Therefore, the construction industry of China should not simply pursue the high-speed growth of the total output value, but pay more attention to high-quality development, such as technological innovation, energy conservation and environmental protection. Finally, the limitations and future research directions are elucidated. Full article
(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)
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14 pages, 1556 KiB  
Article
Novel Fractional Grey Prediction Model with the Change-Point Detection for Overseas Talent Mobility Prediction
by Peng Jiang, Geng Wu, Yi-Chung Hu, Xue Zhang and Yining Ren
Axioms 2022, 11(9), 432; https://doi.org/10.3390/axioms11090432 - 26 Aug 2022
Cited by 2 | Viewed by 1406
Abstract
Overseas students constitute the paramount talent resource for China, and, hence, overseas talent mobility prediction is crucial for the formulation of China’s talent strategy. This study proposes a new model for predicting the number of students studying abroad and returning students, based on [...] Read more.
Overseas students constitute the paramount talent resource for China, and, hence, overseas talent mobility prediction is crucial for the formulation of China’s talent strategy. This study proposes a new model for predicting the number of students studying abroad and returning students, based on the grey system theory, owing to the limited data and uncertainty of the influencing factors. The proposed model introduces change-point detection to determine the number of modeling time points, based on the fractional-order grey prediction model. We employed a change-point detection method to find the change points for determining the model length, based on the principle of new information priority, and used a fractional order accumulated generating operation to construct a grey prediction model. The two real data sets, the annual number of students studying abroad and returning students, were employed to verify the superiority of the proposed model. The results showed that the proposed model outperformed other benchmark models. Furthermore, the proposed model has been employed to predict the tendencies of overseas talent mobility in China by 2025. Further, certain policy recommendations for China’s talent strategy development have been proposed, based on the prediction results. Full article
(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)
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18 pages, 2572 KiB  
Article
Power Consumption Forecast of Three Major Industries in China Based on Fractional Grey Model
by Yuhan Xie, Yunfei Yang and Lifeng Wu
Axioms 2022, 11(8), 407; https://doi.org/10.3390/axioms11080407 - 16 Aug 2022
Cited by 6 | Viewed by 1269
Abstract
As one of the most significant carbon emission departments in China, the power industry will gradually become the core hub of reducing carbon emissions in the process of undertaking carbon emissions transferred from other industries. Therefore, it is of vital importance to predict [...] Read more.
As one of the most significant carbon emission departments in China, the power industry will gradually become the core hub of reducing carbon emissions in the process of undertaking carbon emissions transferred from other industries. Therefore, it is of vital importance to predict the power consumption in China’s end energy consumption to achieve the carbon peak goal on time. This paper firstly uses the gray relational analysis model to study the relationship between power consumption indicators of the three major industries and some social and economic indicators and obtains the influencing factors with the greatest correlation with the power consumption of the three industries. Then, based on the analysis of socio-economic factors, considering different growth rates, the GMCN(1,N) model of electricity consumption in China’s three major industries is established. Forecast data under different scenarios have important practical significance for formulating active and effective energy policies. The data indicate that the secondary and tertiary industries consume the greatest amount of electricity. It is estimated that the power consumption of China’s three major industries will reach 10.15 trillion kWh (kilowatt hours) by 2030. Full article
(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)
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