Pub Date : 2008-06-01DOI: 10.30016/JGS.200806.0007
Zheng-peng Wu, Sifeng Liu, Chuanmin Mi
Based on the present theories of buffer operators, this paper proposed a kind of buffer operator, which all has the universality and practicability. We have proved it to be strengthening buffer operator.
{"title":"Study on the Sequence of Strengthening Buffer Operator Based on the Strictly Monotonic Function","authors":"Zheng-peng Wu, Sifeng Liu, Chuanmin Mi","doi":"10.30016/JGS.200806.0007","DOIUrl":"https://doi.org/10.30016/JGS.200806.0007","url":null,"abstract":"Based on the present theories of buffer operators, this paper proposed a kind of buffer operator, which all has the universality and practicability. We have proved it to be strengthening buffer operator.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056728","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 : 2008-06-01DOI: 10.30016/JGS.200806.0005
Kuo-Yen Lo
This paper presents a multiple criteria decision support approach in order to build a ranking and suggest a best choice1 on a set of alternatives. The decision of how to choose a group of optimal stocks in the stock market is a basic problem in the stock investment process. This research describes a AHP (analytic hierarchy process) to determine the weighting of subjective judgments and a synthetic evaluation system is proposed on the basis of a novel grey multi-hierarchy decision method to select stocks based on their qualitative and quantitative data. The developed tool can be used for in depth analysis of the stock market. First, Analytic hierarchy process (AHP) is using for the decision of weight of multi-hierarchy and multi-facto. Second, fuzzy set theory is used to deal with quantification of qualitative data. Third, the general selection method selects the optimal value or the idealized value from these original data values as the reference data values. Finally, a novel grey relational coefficient calculated reflects the relational degree between single data and reference data. The order of grey relational grades of the aim layer is just the superior and inferior sequence of these stocks. Then the evaluation system is applied to an example. The results show that the evaluation system can overcome the errors of expert's subjective judgment.
{"title":"A Novel Grey Relation Method with Analytic Hierarchy Process for Stock Selection","authors":"Kuo-Yen Lo","doi":"10.30016/JGS.200806.0005","DOIUrl":"https://doi.org/10.30016/JGS.200806.0005","url":null,"abstract":"This paper presents a multiple criteria decision support approach in order to build a ranking and suggest a best choice1 on a set of alternatives. The decision of how to choose a group of optimal stocks in the stock market is a basic problem in the stock investment process. This research describes a AHP (analytic hierarchy process) to determine the weighting of subjective judgments and a synthetic evaluation system is proposed on the basis of a novel grey multi-hierarchy decision method to select stocks based on their qualitative and quantitative data. The developed tool can be used for in depth analysis of the stock market. First, Analytic hierarchy process (AHP) is using for the decision of weight of multi-hierarchy and multi-facto. Second, fuzzy set theory is used to deal with quantification of qualitative data. Third, the general selection method selects the optimal value or the idealized value from these original data values as the reference data values. Finally, a novel grey relational coefficient calculated reflects the relational degree between single data and reference data. The order of grey relational grades of the aim layer is just the superior and inferior sequence of these stocks. Then the evaluation system is applied to an example. The results show that the evaluation system can overcome the errors of expert's subjective judgment.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056666","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 : 2008-06-01DOI: 10.30016/JGS.200806.0002
Yi-Fung Huang, Mei-Li You, Kun-Li Wen
In the prediction research, the main purpose is to minimize the prediction error; however, the goals cannot be fulfilled completely. Even we choose GM (1,1) model, we also need to minimize the prediction error. Hence, in this paper, we first focus on the influence parameter α in GM (1,1) model, then, analyze the characteristics of α step by step. Second, we give up the α=0.5 method, and use numerical method to find the prediction error corresponding with α value and plot the figure of the function of error. Third, for massive data testing, they show that the minimum prediction error does not occur at α=0.5, even not nearly by α=0.5. Fourth, the average prediction error for which the Class Ratio test are fail is sufficient larger than the average prediction error for which the Class Ratio test pass. Finally, after the mathematics model has been presented; we also develop a toolbox, which based on C language to assist us to implement our approach. Consequently, we conclude that the value of α is adaptive in the interval of [0,1] in GM (1,1) model.
{"title":"The Development of GM (1,1) Error Toolbox Based on C Language","authors":"Yi-Fung Huang, Mei-Li You, Kun-Li Wen","doi":"10.30016/JGS.200806.0002","DOIUrl":"https://doi.org/10.30016/JGS.200806.0002","url":null,"abstract":"In the prediction research, the main purpose is to minimize the prediction error; however, the goals cannot be fulfilled completely. Even we choose GM (1,1) model, we also need to minimize the prediction error. Hence, in this paper, we first focus on the influence parameter α in GM (1,1) model, then, analyze the characteristics of α step by step. Second, we give up the α=0.5 method, and use numerical method to find the prediction error corresponding with α value and plot the figure of the function of error. Third, for massive data testing, they show that the minimum prediction error does not occur at α=0.5, even not nearly by α=0.5. Fourth, the average prediction error for which the Class Ratio test are fail is sufficient larger than the average prediction error for which the Class Ratio test pass. Finally, after the mathematics model has been presented; we also develop a toolbox, which based on C language to assist us to implement our approach. Consequently, we conclude that the value of α is adaptive in the interval of [0,1] in GM (1,1) model.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056917","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 : 2008-06-01DOI: 10.30016/JGS.200806.0006
Huan-Bin Xue, Yong Wei
This paper analyzes the reason why there is a error in an optimized GM (1,1) based on connotation expression, though it has improved the modeling precision greatly. Then put forward a solution method for this reason, and obtain a new GM (1,1) model which improves the model precision further. The new model has been proven strictly to have the property of white exponential law coincident, so it not only to be suitable for the low growth sequence, but also suitable for the high growth sequence. Through simulation to a large number of data and comparing with the original GM (1,1) model and the optimized GM (1,1) model based on connotation expression, we discovered that the new optimized model in this paper has a very high simulation and forecasting precision.
{"title":"A Further Optimization in an Optimized Grey GM (1, 1) Model","authors":"Huan-Bin Xue, Yong Wei","doi":"10.30016/JGS.200806.0006","DOIUrl":"https://doi.org/10.30016/JGS.200806.0006","url":null,"abstract":"This paper analyzes the reason why there is a error in an optimized GM (1,1) based on connotation expression, though it has improved the modeling precision greatly. Then put forward a solution method for this reason, and obtain a new GM (1,1) model which improves the model precision further. The new model has been proven strictly to have the property of white exponential law coincident, so it not only to be suitable for the low growth sequence, but also suitable for the high growth sequence. Through simulation to a large number of data and comparing with the original GM (1,1) model and the optimized GM (1,1) model based on connotation expression, we discovered that the new optimized model in this paper has a very high simulation and forecasting precision.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056716","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 : 2007-12-01DOI: 10.30016/JGS.200712.0007
K. Huang, Chuen-Jiuan Jane
This paper illustrates that rough set theory (RS), allied with the use of Grey Prediction, GM(1,N), K-means and Grey Relation, can out-perform the more standard approaches that are employed in economics, such as a Probit model. This study focuses on electron sector stock to select the optimal stock portfolio out applying the financial statement datum from the New Taiwan Economy database(TEJ). Firstly, we collect relative financial ratio datum as the conditional attributes selection and then use GM(1,1) for predicting, GM(1,N) for choosing the more important conditional attributes, and rough set for figuring the best portfolio out. Finally, conduct fund weight distribution using the grey relational method to reduce the investment risk. This study will demonstrate that rough sets model is applicable to stock portfolio. The empirical result in Taiwan: During five years (2003-2007), the average annual rate of return was 20.41%, the accumulated rate of return for nine-quarter was 61.22%. The portfolio determined by the model is a promising alternative to the conventional methods for economic and financial prediction.
{"title":"Portfolio Selection of Electron Sector Stock Based on Rough Set and Grey Theory","authors":"K. Huang, Chuen-Jiuan Jane","doi":"10.30016/JGS.200712.0007","DOIUrl":"https://doi.org/10.30016/JGS.200712.0007","url":null,"abstract":"This paper illustrates that rough set theory (RS), allied with the use of Grey Prediction, GM(1,N), K-means and Grey Relation, can out-perform the more standard approaches that are employed in economics, such as a Probit model. This study focuses on electron sector stock to select the optimal stock portfolio out applying the financial statement datum from the New Taiwan Economy database(TEJ). Firstly, we collect relative financial ratio datum as the conditional attributes selection and then use GM(1,1) for predicting, GM(1,N) for choosing the more important conditional attributes, and rough set for figuring the best portfolio out. Finally, conduct fund weight distribution using the grey relational method to reduce the investment risk. This study will demonstrate that rough sets model is applicable to stock portfolio. The empirical result in Taiwan: During five years (2003-2007), the average annual rate of return was 20.41%, the accumulated rate of return for nine-quarter was 61.22%. The portfolio determined by the model is a promising alternative to the conventional methods for economic and financial prediction.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056371","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 : 2007-09-01DOI: 10.30016/JGS.200709.0006
C. Kung, Chen-Kuo Lee, Chin-Ming Wang, Tzung-Ming Yan
As Vietnam has been taking active measures to improve its environment for FDI (foreign direct investment) in recent years, more and more Taiwanese manufacturers show their presence there. However, there was little empirical research devoted to industrial investment in Vietnam owing to difficult sampling and data acquisition. Meanwhile, traditional probability statistical method could not make sense in this aspect. As an innovative method, Grey Theory could help to analyze small samples from Taiwanese manufacturers in Vietnam. This paper attempted to acquire major influential dimensions and variables to the entry mode of Taiwan manufacturers, and then determine the ranking of their overall performance using Grey Situation Decision-Making method. Finally, GM(0,N) model was used to analyze the recognition degree of different manufacturers for the entry mode. It is thus learnt that different industries, such as handicraft and leather bag, have different recognition degrees on the entry mode, thus providing a reference for foreign investors.
{"title":"Evaluation of Entry Mode of Overseas Investment Using Grey Relation Method","authors":"C. Kung, Chen-Kuo Lee, Chin-Ming Wang, Tzung-Ming Yan","doi":"10.30016/JGS.200709.0006","DOIUrl":"https://doi.org/10.30016/JGS.200709.0006","url":null,"abstract":"As Vietnam has been taking active measures to improve its environment for FDI (foreign direct investment) in recent years, more and more Taiwanese manufacturers show their presence there. However, there was little empirical research devoted to industrial investment in Vietnam owing to difficult sampling and data acquisition. Meanwhile, traditional probability statistical method could not make sense in this aspect. As an innovative method, Grey Theory could help to analyze small samples from Taiwanese manufacturers in Vietnam. This paper attempted to acquire major influential dimensions and variables to the entry mode of Taiwan manufacturers, and then determine the ranking of their overall performance using Grey Situation Decision-Making method. Finally, GM(0,N) model was used to analyze the recognition degree of different manufacturers for the entry mode. It is thus learnt that different industries, such as handicraft and leather bag, have different recognition degrees on the entry mode, thus providing a reference for foreign investors.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056127","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 : 2007-09-01DOI: 10.30016/JGS.200709.0007
R. Guo, D. Guo, G. Midgley, A. Rebelo
In this paper, we merge partial differential equation model, regression model and credibility measure based fuzzy mathematics proposed by Liu into a new partial differential equation motivated regression model (abbreviated as PDEMR model). The creation of PDEMR model further extends DEMR model ideation proposed by Guo et al. Furthermore, we develop a PDEMR model for the quantitative modeling on multivariate small sample data. PDEMR models will be able to establish the quantitative relationship among the main factor vector and the covariate vectors, which is a major improvement of information extraction with sparse data availability. Finally, we apply the PDEMR model to South African rare Protea species predictions and even tune up the data set for a regional GIS kriging maps.
{"title":"PDEMR Model in Rare Protea Count Prediction","authors":"R. Guo, D. Guo, G. Midgley, A. Rebelo","doi":"10.30016/JGS.200709.0007","DOIUrl":"https://doi.org/10.30016/JGS.200709.0007","url":null,"abstract":"In this paper, we merge partial differential equation model, regression model and credibility measure based fuzzy mathematics proposed by Liu into a new partial differential equation motivated regression model (abbreviated as PDEMR model). The creation of PDEMR model further extends DEMR model ideation proposed by Guo et al. Furthermore, we develop a PDEMR model for the quantitative modeling on multivariate small sample data. PDEMR models will be able to establish the quantitative relationship among the main factor vector and the covariate vectors, which is a major improvement of information extraction with sparse data availability. Finally, we apply the PDEMR model to South African rare Protea species predictions and even tune up the data set for a regional GIS kriging maps.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056169","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 : 2007-09-01DOI: 10.30016/JGS.200709.0003
J. Usuki, M. Kitaoka
Circular data can be expressed as circular diagram for time series data. This study presents the computational procedure, which made circular diagram for the data with periodicity. The method for displaying circular diagram using spline function and GM(1,1) model of the Grey Theory is developed to analyze the periodic data. In addition, the method for displaying the fluctuation of the periodic data from least squares method, GM(1,1) model and periodic spline function is shown.
{"title":"Circular Data Analysis of Periodic Time Series Data Using Grey Theory","authors":"J. Usuki, M. Kitaoka","doi":"10.30016/JGS.200709.0003","DOIUrl":"https://doi.org/10.30016/JGS.200709.0003","url":null,"abstract":"Circular data can be expressed as circular diagram for time series data. This study presents the computational procedure, which made circular diagram for the data with periodicity. The method for displaying circular diagram using spline function and GM(1,1) model of the Grey Theory is developed to analyze the periodic data. In addition, the method for displaying the fluctuation of the periodic data from least squares method, GM(1,1) model and periodic spline function is shown.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056400","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 : 2007-09-01DOI: 10.30016/JGS.200709.0001
Kuo-Chen Hung, Fu-Yuan Hsu, Kuo-Jung Wu, Kun-Li Wen, John H. Wu
The aim of this paper is to improve the GM(1,1) predictive model that has been originally developed by Deng in 1982. It is a non-statistic prediction model with very few original data, there has been applied in different fields. However, from the original grey predictive model, we find two problems, (1) applying the GM(1,1) model to predict maybe obtained the result of decreasing trend, this result violate hypothesis of exponential increase trend, (2) the first point of original data is different with 1st point of predictive value that both exist an error term. Therefore, we improved the problem of decreasing trend and provide a newly modified model. Moreover, we proposed an enhanced GM(1,1) grey prediction approach that adopted modified error terms for each original data point mapping into each predictive point to fit the actual value. Meanwhile, in this paper, we applying this enhanced model to predict electricity demand, and comparison with Deng's prediction model, the analyzed results demonstrate the usefulness of this study.
{"title":"An Enhanced GM(1,1) Grey Prediction Approach with Error Term μ(k)","authors":"Kuo-Chen Hung, Fu-Yuan Hsu, Kuo-Jung Wu, Kun-Li Wen, John H. Wu","doi":"10.30016/JGS.200709.0001","DOIUrl":"https://doi.org/10.30016/JGS.200709.0001","url":null,"abstract":"The aim of this paper is to improve the GM(1,1) predictive model that has been originally developed by Deng in 1982. It is a non-statistic prediction model with very few original data, there has been applied in different fields. However, from the original grey predictive model, we find two problems, (1) applying the GM(1,1) model to predict maybe obtained the result of decreasing trend, this result violate hypothesis of exponential increase trend, (2) the first point of original data is different with 1st point of predictive value that both exist an error term. Therefore, we improved the problem of decreasing trend and provide a newly modified model. Moreover, we proposed an enhanced GM(1,1) grey prediction approach that adopted modified error terms for each original data point mapping into each predictive point to fit the actual value. Meanwhile, in this paper, we applying this enhanced model to predict electricity demand, and comparison with Deng's prediction model, the analyzed results demonstrate the usefulness of this study.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70056344","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 : 2007-09-01DOI: 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":null,"pages":null},"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}
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