Pub Date : 2007-09-01DOI: 10.30016/JGS.200709.0004
Xiaoxuan Zhang
This paper reveals that GM(1,1) model is actually constructed according to the first order linearly differential equation, it is an equation that exponential sequences satisfy, so the essential of GM(1,1) model is an exponential sequence model. Though GM(1,1) model is constructed according to the first order linearly differential equation, both are not the same, this paper shows their features in common and differences. In addition, this paper proposes that models constructed according to the first order linearly differential equation are not unique, the author constructs another exponential sequence model, we might as well call it grey exponential model(GEM), it can replace GM(1,1) model for predicting of grey systems.
{"title":"The Essential of GM(1,1) Model","authors":"Xiaoxuan Zhang","doi":"10.30016/JGS.200709.0004","DOIUrl":"https://doi.org/10.30016/JGS.200709.0004","url":null,"abstract":"This paper reveals that GM(1,1) model is actually constructed according to the first order linearly differential equation, it is an equation that exponential sequences satisfy, so the essential of GM(1,1) model is an exponential sequence model. Though GM(1,1) model is constructed according to the first order linearly differential equation, both are not the same, this paper shows their features in common and differences. In addition, this paper proposes that models constructed according to the first order linearly differential equation are not unique, the author constructs another exponential sequence model, we might as well call it grey exponential model(GEM), it can replace GM(1,1) model for predicting of grey systems.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"81-87"},"PeriodicalIF":1.6,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-06-01DOI: 10.30016/JGS.200706.0005
D. Yamaguchi, GuoDong Li, Kozo Mizutani Takahiro Akabane, M. Nagai, M. Kitaoka
Grey Structural Modeling (GSM for short) is a new approach of system modeling method succeeding to ISM and FSM. GSM is based on the two procedures: estimating a hierarchy of the elements and estimating paths among the elements. The former is constructed from complex equations including set operation. In this paper, a significant algorithm of the GSM procedure is presented for reliable implementation. The main problem we should solve is how to group the elements into several classes and to determine their hierarchy in the computation. First of all, these procedures are shown in a pseudo language with several figures. The main idea is that two new arrays are defined to manage the elements of hierarchy, and the set operation is founded on the matrix and those arrays computation. Three examples in decision-making are shown with the developed program. The result shows that this algorithm is reliable and the developed program is useful for decision-making.
{"title":"A Realization Algorithm of Grey Structural Modeling","authors":"D. Yamaguchi, GuoDong Li, Kozo Mizutani Takahiro Akabane, M. Nagai, M. Kitaoka","doi":"10.30016/JGS.200706.0005","DOIUrl":"https://doi.org/10.30016/JGS.200706.0005","url":null,"abstract":"Grey Structural Modeling (GSM for short) is a new approach of system modeling method succeeding to ISM and FSM. GSM is based on the two procedures: estimating a hierarchy of the elements and estimating paths among the elements. The former is constructed from complex equations including set operation. In this paper, a significant algorithm of the GSM procedure is presented for reliable implementation. The main problem we should solve is how to group the elements into several classes and to determine their hierarchy in the computation. First of all, these procedures are shown in a pseudo language with several figures. The main idea is that two new arrays are defined to manage the elements of hierarchy, and the set operation is founded on the matrix and those arrays computation. Three examples in decision-making are shown with the developed program. The result shows that this algorithm is reliable and the developed program is useful for decision-making.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"33-40"},"PeriodicalIF":1.6,"publicationDate":"2007-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-06-01DOI: 10.30016/JGS.200706.0001
Li-Chu Hung
We examine the accuracy of the model with empirical study focusing on regression analysis in econometric model. Then we compare the result from the model and that from the four GM (1, 1) shadow models in grey forecast. To appraise the ability of the forecasting model, we use MAPE (Mean Absolute Percentage Error) to examine the accuracy of the model. We find all the MAPE values are between 10~20, which yield an excellent forecasting ability. Though the values forecasted by 4 GM (1, 1) shadow models are larger than those from the forecasting model built by this research, they are within the scope excellent forecasting ability to prove that we can replace econometric regression forecasting model with grey forecast partially.
{"title":"The Study of Grey Forecasting in Replacement for Economic Forecasting Model","authors":"Li-Chu Hung","doi":"10.30016/JGS.200706.0001","DOIUrl":"https://doi.org/10.30016/JGS.200706.0001","url":null,"abstract":"We examine the accuracy of the model with empirical study focusing on regression analysis in econometric model. Then we compare the result from the model and that from the four GM (1, 1) shadow models in grey forecast. To appraise the ability of the forecasting model, we use MAPE (Mean Absolute Percentage Error) to examine the accuracy of the model. We find all the MAPE values are between 10~20, which yield an excellent forecasting ability. Though the values forecasted by 4 GM (1, 1) shadow models are larger than those from the forecasting model built by this research, they are within the scope excellent forecasting ability to prove that we can replace econometric regression forecasting model with grey forecast partially.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"1-7"},"PeriodicalIF":1.6,"publicationDate":"2007-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-06-01DOI: 10.30016/JGS.200706.0007
Meng Lu, K. Wevers
Grey system theory was initiated in the beginning of 1980s. Since then the research on theory development and applications is progressing. However, until today nearly all researchers of grey system theory are from Chinese speaking areas, and the theory is still hardly known nor accepted in the western world. The paper addresses the state-of-the-art development of grey system theory and its application. It aims to highlight and analyse relevant issues (i.e. obstacles, possible solutions and potential trends) for further research from the perspective both of grey system theory and of the grey system methods.
{"title":"Grey System Theory and Applications: A Way Forward","authors":"Meng Lu, K. Wevers","doi":"10.30016/JGS.200706.0007","DOIUrl":"https://doi.org/10.30016/JGS.200706.0007","url":null,"abstract":"Grey system theory was initiated in the beginning of 1980s. Since then the research on theory development and applications is progressing. However, until today nearly all researchers of grey system theory are from Chinese speaking areas, and the theory is still hardly known nor accepted in the western world. The paper addresses the state-of-the-art development of grey system theory and its application. It aims to highlight and analyse relevant issues (i.e. obstacles, possible solutions and potential trends) for further research from the perspective both of grey system theory and of the grey system methods.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"47-53"},"PeriodicalIF":1.6,"publicationDate":"2007-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-06-01DOI: 10.30016/JGS.200706.0004
Shuo-Pei Chen, C. Shih
As market competition intensifies, most companies realize that they have to constantly develop new products to survive the competition. Though there is always a great risk involved with product development. The accurate anticipation of product diffusion will help reduce the risk of blind investment. In this study a comprehensive procedure for analyzing the diffusion of new product launching is proposed. The new procedure is comprised of two stages: (a) first the major factors that influence the diffusion of products most are identified using the grey relational analysis and (b) secondly an improved grey prediction model is then used to predict the product diffusion based on the selected factors. The improved grey prediction model, called the GMC model, uses convolution integration to promote the forecasting ability of the traditional GM model. The diffusion data of several product categories are examined. The results show that different major macroeconomic indices need to be used in the prediction model according to whether the goods are durable or non-durable. The inclusion of these macroeconomic indices in the GMC model can significantly improve the prediction accuracy. The proposed procedure can help companies improve their prediction ability and provide managers with more marketing information.
{"title":"Diffusion Forecasting of Innovative Products Using an Improved Grey Model","authors":"Shuo-Pei Chen, C. Shih","doi":"10.30016/JGS.200706.0004","DOIUrl":"https://doi.org/10.30016/JGS.200706.0004","url":null,"abstract":"As market competition intensifies, most companies realize that they have to constantly develop new products to survive the competition. Though there is always a great risk involved with product development. The accurate anticipation of product diffusion will help reduce the risk of blind investment. In this study a comprehensive procedure for analyzing the diffusion of new product launching is proposed. The new procedure is comprised of two stages: (a) first the major factors that influence the diffusion of products most are identified using the grey relational analysis and (b) secondly an improved grey prediction model is then used to predict the product diffusion based on the selected factors. The improved grey prediction model, called the GMC model, uses convolution integration to promote the forecasting ability of the traditional GM model. The diffusion data of several product categories are examined. The results show that different major macroeconomic indices need to be used in the prediction model according to whether the goods are durable or non-durable. The inclusion of these macroeconomic indices in the GMC model can significantly improve the prediction accuracy. The proposed procedure can help companies improve their prediction ability and provide managers with more marketing information.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"23-32"},"PeriodicalIF":1.6,"publicationDate":"2007-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-06-01DOI: 10.30016/JGS.200706.0003
Xin-ping Xiao, Xiaoxuan Zhang
The inertia is an essential characteristic of an energy system. For adapting to the need of modeling for generalized energy systems such as society, economy and technology etc, the inertia grey modeling theory that has considered inertia and inspirit of the system has a significant prospect in application. In this paper, we propose a new way to set up the inertia grey modeling theory based on the matrix analysis. Sequentially, we study the expressions of the force elements of various orders in the system of matrices, and express the raw series, AGO generating series and mean generating series with force elements respectively. Meanwhile, we also obtain the mathematical structure of the force space and properties of the decomposed transformations. It is shown that the inertia grey modeling can be represented in simplified matrix forms.
{"title":"The Inertia Grey Modeling Theory Based on Matrix Analysis","authors":"Xin-ping Xiao, Xiaoxuan Zhang","doi":"10.30016/JGS.200706.0003","DOIUrl":"https://doi.org/10.30016/JGS.200706.0003","url":null,"abstract":"The inertia is an essential characteristic of an energy system. For adapting to the need of modeling for generalized energy systems such as society, economy and technology etc, the inertia grey modeling theory that has considered inertia and inspirit of the system has a significant prospect in application. In this paper, we propose a new way to set up the inertia grey modeling theory based on the matrix analysis. Sequentially, we study the expressions of the force elements of various orders in the system of matrices, and express the raw series, AGO generating series and mean generating series with force elements respectively. Meanwhile, we also obtain the mathematical structure of the force space and properties of the decomposed transformations. It is shown that the inertia grey modeling can be represented in simplified matrix forms.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"10 1","pages":"17-22"},"PeriodicalIF":1.6,"publicationDate":"2007-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-01DOI: 10.30016/JGS.200612.0007
Chang-Jo Wu, Fu-Yuan Hsu, Kun-Li Wen, John H. Wu
In the GM (1,1) study, generally speaking, the original data are non-smoothing type. But, actually, many types of data are smoothing and nonlinear. Such as population model, that is shown the saturation behavior in where. Hence, Deng and Wen proposed Verhulst model in GM (1,1) model to analyze this type of original data. However, the formula has some missing. Therefore, in this paper, we not only present the novel application for GM(1,1|α) to solve the problem, but also suggest the 4-points rolling in GM(1,1|α) is the better method in this field.
{"title":"The Study of GM (1,1|α) on the Verhulst Model","authors":"Chang-Jo Wu, Fu-Yuan Hsu, Kun-Li Wen, John H. Wu","doi":"10.30016/JGS.200612.0007","DOIUrl":"https://doi.org/10.30016/JGS.200612.0007","url":null,"abstract":"In the GM (1,1) study, generally speaking, the original data are non-smoothing type. But, actually, many types of data are smoothing and nonlinear. Such as population model, that is shown the saturation behavior in where. Hence, Deng and Wen proposed Verhulst model in GM (1,1) model to analyze this type of original data. However, the formula has some missing. Therefore, in this paper, we not only present the novel application for GM(1,1|α) to solve the problem, but also suggest the 4-points rolling in GM(1,1|α) is the better method in this field.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"9 1","pages":"131-138"},"PeriodicalIF":1.6,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70055840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-01DOI: 10.30016/JGS.200612.0005
Sifeng Liu, Zhigeng Fang, Yi Lin
Based on the definition of degree of grey incidence, which put forward by Professor Ju-Long Deng, a new definition of absolute degree of grey incidence is given in this paper. And a simplified method to calculate the new absolute degree of grey incidence is put forward and proved. The properties of the new definition of absolute degree of grey incidence are studied. Compared with the original definition, the new definition has many advantages such as (1) satisfies the properties of symmetry, (2) the order of grey incidences remain stable, and (3) with smaller amount of computation, etc.
{"title":"Study on a New Definition of Degree of Grey Incidence","authors":"Sifeng Liu, Zhigeng Fang, Yi Lin","doi":"10.30016/JGS.200612.0005","DOIUrl":"https://doi.org/10.30016/JGS.200612.0005","url":null,"abstract":"Based on the definition of degree of grey incidence, which put forward by Professor Ju-Long Deng, a new definition of absolute degree of grey incidence is given in this paper. And a simplified method to calculate the new absolute degree of grey incidence is put forward and proved. The properties of the new definition of absolute degree of grey incidence are studied. Compared with the original definition, the new definition has many advantages such as (1) satisfies the properties of symmetry, (2) the order of grey incidences remain stable, and (3) with smaller amount of computation, etc.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"9 1","pages":"115-122"},"PeriodicalIF":1.6,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70055637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-01DOI: 10.30016/JGS.200612.0004
GuoDong Li, D. Yamaguchi, M. Nagai, M. Kitaoka
Grey Model (GM) based on grey system theory has already been established as a prediction model in 1982. At present, it has been applied to many fields. However, in the traditional GM, the calculation methods of derivative value d(superscript n) x/dt(superscript n) and background value z are obtained by the analysis of observed white value. Therefore, it influenced the calculation of coefficient â and the prediction accuracy of the traditional GM is unsatisfied. Especially, the prediction accuracy falls in case of the multi-variable or multi-dimensional greatly. In this paper, a new calculation method of derivative value d(superscript n) x/dt(superscript n) and background value z is proposed according to cubic spline function and Taylor approximation method and it is analyzed by grey interval analysis. We obtain the new calculation method of coefficient â by the proposal GM, and this new model is defined as T-3spGM. We present two specific examples; the prediction accuracy of proposal model is verified. As the results, we report that the prediction accuracy of the proposal new model was raised greatly.
{"title":"A Research on Grey Model by Grey Interval Analysis","authors":"GuoDong Li, D. Yamaguchi, M. Nagai, M. Kitaoka","doi":"10.30016/JGS.200612.0004","DOIUrl":"https://doi.org/10.30016/JGS.200612.0004","url":null,"abstract":"Grey Model (GM) based on grey system theory has already been established as a prediction model in 1982. At present, it has been applied to many fields. However, in the traditional GM, the calculation methods of derivative value d(superscript n) x/dt(superscript n) and background value z are obtained by the analysis of observed white value. Therefore, it influenced the calculation of coefficient â and the prediction accuracy of the traditional GM is unsatisfied. Especially, the prediction accuracy falls in case of the multi-variable or multi-dimensional greatly. In this paper, a new calculation method of derivative value d(superscript n) x/dt(superscript n) and background value z is proposed according to cubic spline function and Taylor approximation method and it is analyzed by grey interval analysis. We obtain the new calculation method of coefficient â by the proposal GM, and this new model is defined as T-3spGM. We present two specific examples; the prediction accuracy of proposal model is verified. As the results, we report that the prediction accuracy of the proposal new model was raised greatly.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"9 1","pages":"103-113"},"PeriodicalIF":1.6,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70055063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-01DOI: 10.30016/JGS.200612.0006
Tsuilin Kuo, Li-Hui Chen
Companies currently face increased competition and shortened product life cycles. Cost information that allows managers to make concise and rapid decisions efficiently of priority concern. Using Grey relational analysis, this study describes cost driver selection model based on an activity-based costing system. Analysis results indicate that the Grey relational analysis can obtain an optimal cost driver using only limited data. Compared with the regression model, Grey relational analysis is more time efficient and requires fewer statistics. Results of this study demonstrate that the proposed model can effectively assist managers in selecting a cost driver.
{"title":"Cost Driver Decision Methods for an Activity-based Cost System","authors":"Tsuilin Kuo, Li-Hui Chen","doi":"10.30016/JGS.200612.0006","DOIUrl":"https://doi.org/10.30016/JGS.200612.0006","url":null,"abstract":"Companies currently face increased competition and shortened product life cycles. Cost information that allows managers to make concise and rapid decisions efficiently of priority concern. Using Grey relational analysis, this study describes cost driver selection model based on an activity-based costing system. Analysis results indicate that the Grey relational analysis can obtain an optimal cost driver using only limited data. Compared with the regression model, Grey relational analysis is more time efficient and requires fewer statistics. Results of this study demonstrate that the proposed model can effectively assist managers in selecting a cost driver.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"9 1","pages":"123-129"},"PeriodicalIF":1.6,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70055685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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