Xinping Xiao and Fuqin Li
The purpose of this paper is to deal with the ill‐conditioned problem for the non‐equigap GM(1,1) control model by using the method of multiple transformations.
Abstract
Purpose
The purpose of this paper is to deal with the ill‐conditioned problem for the non‐equigap GM(1,1) control model by using the method of multiple transformations.
Design/methodology/approach
Owing to noises and interferences from both inside and outside of the system, many control systems contain unequal intervals and sharp variation which may result in undesirable systems instability. In order to ensure the stability and efficiency of grey forecasting control model, the data transformation for a raw series is an important and useful method for enhancing accuracy and improving ill‐condition of the non‐equigap GM(1,1) model.
Findings
This paper discusses the quantitative relations between the multiple transformation and the parameters of the non‐equigap GM(1,1) model in detail, and studies the effect of the multiple transformation on the condition number of the non‐equigap GM(1,1) model.
Research limitations/implications
Accessibility and availability of data are the main limitations based on which model will be applied.
Practical implications
Choosing an appropriate multiple of transformation cannot only eliminate dimension, lessen computation and maintain high accuracy, but also largely reduce the condition number of the model and improve the ill‐condition of non‐equigap GM(1,1) model effectively.
Originality/value
This paper seems to be the first to discuss the stability problems for the non‐equigap GM(1,1) model.
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Xinping Xiao and Yayun Lu
The purpose of this paper is to simplify the computation of parameter estimation in the grey linear regression model and solve the problem that the development coefficient could…
Abstract
Purpose
The purpose of this paper is to simplify the computation of parameter estimation in the grey linear regression model and solve the problem that the development coefficient could not be computed in some sequence data, such as short‐term traffic flow.
Design/methodology/approach
Starting from the limitation that can be identified in the equation and analyzing the range using the method to estimate parameters, this paper researches the modelling mechanism and the other forms which are equivalent with the original form. At the same time, this paper gives an estimation method and gets the relationship in various forms and the relationship between the model and GM(1,1) model.
Findings
For the grey linear regression model, there exists a new method of parameter identification and three other forms as follows: the original form, the Whitenization equation and the connotation form.
Practical implications
The method of parameter identification exposed in the paper expanded the scope of the application of the grey linear regression model, and it can be used to model and forecast the urban road short‐time traffic flow.
Originality/value
This paper has solved some complicated problems such as the parameter estimation computation in the grey linear regression model. In addition, three kinds of representation forms of the model and its relationship between the model and GM(1,1) have also been presented. Finally, its application of the model in a short‐term traffic flow prediction has shown its superiority.
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The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.
Abstract
Purpose
The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.
Design/methodology/approach
Generalized non‐equidistance GM(1,1) model is put forward based on generalized accumulated generating operation (AGO) theory, and particle swarm optimization is used to solve the parameters of the new model, then affine properties of the new model are researched based on matrix analysis.
Findings
The results are convincing: the simulation and prediction precisions of generalized non‐equidistance GM(1,1) model are raised greatly, and it is proved that the affine transformation sequence has the same simulative accuracy with the raw sequence for generalized non‐equidistance GM(1,1) model.
Practical implications
The method exposed in the paper can be used to model and predict for non‐equidistance sequence in the practical problem.
Originality/value
The paper succeeds in establishing a new non‐equidistance grey model and obtaining the affine properties of generalized non‐equidistance GM(1,1) model.
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Sifeng Liu, Yingjie Yang, Ying Cao and Naiming Xie
The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.
Abstract
Purpose
The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.
Design/methodology/approach
Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.
Findings
The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.
Originality/value
The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.
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Changhai Lin, Zhengyu Song, Sifeng Liu, Yingjie Yang and Jeffrey Forrest
The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the…
Abstract
Purpose
The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.
Design/methodology/approach
The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.
Findings
Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.
Practical implications
The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.
Originality/value
The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.
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Wei Meng, Qian Li, Bo Zeng and Yingjie Yang
The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with…
Abstract
Purpose
The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with the unified fractional grey generation operator.
Design/methodology/approach
By systematically studying the properties of the fractional accumulating operator and the reducing operator, and analyzing the sensitivity of the order value, a unified expression of the fractional operators is given. The FDGM(1,1) model with the unified fractional grey generation operator is established. The relationship between the order value and the modeling error distribution is studied.
Findings
The expression of the fractional accumulating generation operator and the reducing generation operator can be unified to a simple expression. For −1<r < 1, the fractional grey generation operator satisfies the principle of new information priority. The DGM(1,1) model is a special case of the FDGM(1,1) model with r = 1.
Research limitations/implications
The sensitivity of the unified operator is verified through random numerical simulation method, and the theoretical proof was not yet possible.
Practical implications
The FDGM(1,1) model has a higher modeling accuracy and modeling adaptability than the DGM(1,1) by optimizing the order.
Originality/value
The expression of the fractional accumulating generation operator and the reducing generation operator is firstly unified. The FDGM(1,1) model with the unified fractional grey generation operator is firstly established. The unification of the fractional accumulating operator and the reducing operator improved the theoretical basis of grey generation operator.
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Sifeng Liu, Yong Tao, Naiming Xie, Liangyan Tao and Mingli Hu
The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it…
Abstract
Purpose
The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.
Design/methodology/approach
Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.
Findings
More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.
Practical implications
It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.
Originality/value
Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.
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Liangyan Tao, Ailin Liang, Naiming Xie and Sifeng Liu
The year 2022 marks the 40th anniversary of the establishment of the grey system theory (GST), which has been widely applied in the engineering field. This paper aims to…
Abstract
Purpose
The year 2022 marks the 40th anniversary of the establishment of the grey system theory (GST), which has been widely applied in the engineering field. This paper aims to systematically identify the achievements, hotspots, knowledge structure and emerging trends in this field.
Design/methodology/approach
A bibliometrics analysis was conducted on relevant publications retrieved from Web of Science (WoS) using CiteSpace and MapEquation. A statistical analysis of the collected 3,384 papers was completed. Three networks, including a co-occurrence network, cooperation network and co-citation network, were obtained to draw knowledge structure, hotspots and research frontiers.
Findings
The top four applied engineering fields are engineering electrical electronics, computer science artificial intelligence, engineering multi-disciplinary and automation control system. In total, 65 countries have engaged in this field, and China has occupied a leading position, with the largest number of articles published and the widest cooperation with other countries. The USA, United Kingdom (UK) and China Taiwan also contribute a lot. The Nanjing University of Aeronautics and Astronautics and Professor Liu Sifeng have a core position in the cooperation network. More hotspots appear in the last ten years. Regarding the emerging trends, the combination of theoretical models and practical engineering problems has attracted more attention. Besides, the application of GST in environment protection and the integration of the GST and intelligent algorithm became more popular.
Originality/value
The comprehensive bibliometrics analysis and visualization demonstration were conducted, presenting the interdisciplinary characteristics, major research topics and research frontiers in this field.
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Li Junliang, Liao Ruiquan and Chen Xiaochun
In practical engineering, there are various sequences. The purpose of this paper is to improve and put forward a new model.
Abstract
Purpose
In practical engineering, there are various sequences. The purpose of this paper is to improve and put forward a new model.
Design/methodology/approach
Based on the generalized accumulated generating operation, the paper improved the GM(1,1) cosine model and proposed the GAGM(1,1) cosine model.
Findings
It is found that the GAGM(1,1) cosine model can satisfy many kinds of periodic sequences and the precision of GAGM(1,1) cosine model is higher than the GM(1,1) model.
Originality/value
The paper shows that the GAGM(1,1) cosine model has important theoretic and practical significance.
Details
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Qiongwei Ye and Baojun Ma
Internet + and Electronic Business in China is a comprehensive resource that provides insight and analysis into E-commerce in China and how it has revolutionized and continues to…
Abstract
Internet + and Electronic Business in China is a comprehensive resource that provides insight and analysis into E-commerce in China and how it has revolutionized and continues to revolutionize business and society. Split into four distinct sections, the book first lays out the theoretical foundations and fundamental concepts of E-Business before moving on to look at internet+ innovation models and their applications in different industries such as agriculture, finance and commerce. The book then provides a comprehensive analysis of E-business platforms and their applications in China before finishing with four comprehensive case studies of major E-business projects, providing readers with successful examples of implementing E-Business entrepreneurship projects.
Internet + and Electronic Business in China is a comprehensive resource that provides insights and analysis into how E-commerce has revolutionized and continues to revolutionize business and society in China.