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Journal ArticleDOI

Introduction to Grey system theory

01 Nov 1989-Journal of Grey System (Sci-Tech Information Services)-Vol. 1, Iss: 1, pp 1-24
TL;DR: The Grey Systeni and its applications are interdisciplinary, cutting across a variety of specialized fields, and it is evident that Grey System theory stands the test of time since 1982 as mentioned in this paper.
Abstract: Grey System theory was initiated in 1982 [7]. As far as information is concerned, the systems which lack information, such as structure message, operation mechanism and behaviour document, are referred to as Grey Systems. For example, the human body, agriculture, economy, etc., are Grey Systems. Usually, on the grounds of existing grey relations, grey elements, grey numbers (denoted by 8 ) one can identify which Grey System is, where \"grey\" means poor, incomplete, uncertain, etc. The goal of Grey Systeni and its applications is to bridge the gap existing between social science and natural science. Thus, one can say that the Grey System theory is interdisciplinary, cutting across a variety of specialized fields, and it is evident that Grey System theory stands the test of time since 1982. As the case stands, the developn~ent of the Grey System-as well as theoretical topic-is coupled with clear applications of the theory in assorted fields. The conccept of the Grey System, in its theory and successful application, is now well known in China. The application fields of the Grey System involve agriculture [23, 77-81, 911, ecology [59], economy [61, 102, 103, 1041, meteorology [58, 74,911, medicine [55, 891, history [63, 641, geography [I], industry [61, earthquake [73, 87, 881, geology [76, 1 191, hydrology [98, 1 121, irrigation strategy [261, military affairs, sports [116], traffic [67], management [30, 97, 1051, material science [82, 831, environment [ 1081, biological protection [69,70], judicial system [loo], etc. Projects which have been successfully completed with the Grey System theory and its applications are as follows: 1. Regional econonlic planning for several provinces in China; 2. To forecast yields of grain for some provinces in China:
Citations
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Journal ArticleDOI
TL;DR: This paper recapitulates the definition given by Atanassov (1983) of intuitionistic fuzzy sets as well as the definition of vague sets given by Gau and Byehrer (1993) and sees that both definitions coincide.

880 citations

Journal ArticleDOI
TL;DR: A systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection is provided by using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches.
Abstract: Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.

825 citations


Cites background or methods from "Introduction to Grey system theory"

  • ...Several emerging AI techniques, including SVM, AR, ACA, and DST, necessitate more transfer learning on future works....

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  • ...Dogan and Aydin (2011) as well as Ferreira and Borenstein (2012) introduced BN for handling existing uncertainty....

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  • ...For SS, Wu (2009b) extended the DST to aggregate individual preferences into a collective preference....

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  • ...(2009) Fuzzy PSO Xu and Yan (2011) Fuzzy DST Deng and Chan (2011)...

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  • ...DST is an uncertainty reasoning tool (Thierry, 1997) that can be used to combine unexpected empirical evidence regarding an individual’s opinion and consequently organize a coherent picture of reality....

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Journal ArticleDOI
TL;DR: This work expands on a novel approach to supplier selection modeling first introduced by (Li et al., 2008), which utilizes grey system and rough set theory and offers insights into the technique with some sensitivity analysis.

775 citations

Journal ArticleDOI
TL;DR: The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting, and the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting.
Abstract: Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, the lack of ability of conventional analysis methods to forecast time series that are not smooth leads the scientists and researchers to resort to various forecasting models that have different mathematical backgrounds, such as artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, the accuracies of different grey models such as GM(1,1), Grey Verhulst model, modified grey models using Fourier Series is investigated. Highly noisy data, the United States dollar to Euro parity between the dates 01.01.2005 and 30.12.2007, are used to compare the performances of the different models. The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting. Among these grey models, the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting.

720 citations


Cites background or methods from "Introduction to Grey system theory"

  • ...(14) is xð0ÞðkÞ þ azð1ÞðkÞ ¼ bðzð1ÞðkÞÞ2; ð15Þ xð0ÞðkÞ ¼ azð1ÞðkÞ þ bðzð1ÞðkÞÞ2: ð16Þ Similar to the GM(1,1) model ½a; b T ¼ ðBT BÞ 1BT Y; ð17Þ where Y ¼ ½xð0Þð2Þ; xð0Þð3Þ; . . . ; xð0ÞðnÞ T ; ð18Þ B ¼ zð1Þð2Þ ðzð1Þð2ÞÞ2 zð1Þð3Þ ðzð1Þð3ÞÞ2 zð1ÞðnÞ ðzð1ÞðnÞÞ2 2 6666666664 3 7777777775 : ð19Þ The solution of xð1ÞðtÞ at time k: xð1Þp ðkþ 1Þ ¼ axð0Þð1Þ bxð0Þð1Þ þ ða bxð0Þð1ÞÞeak : ð20Þ Applying the IAGO, the solution of xð0ÞðtÞ at time k: xð0Þp ðkÞ ¼ axð0Þð1Þða bxð0Þð1ÞÞ ðbxð0Þð1Þ þ ða bxð0Þð1ÞÞeaðk 1ÞÞ ð1 e aÞeaðk 2Þ ðbxð0Þð1Þ þ ða bxð0Þð1ÞÞeaðk 2ÞÞ : ð21Þ As can be seen, in Eq....

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  • ...(7), the solution of xð1ÞðtÞ at time k: xð1Þp ðkþ 1Þ ¼ xð0Þð1Þ b a e ak þ b a : ð11Þ To obtain the predicted value of the primitive data at time (k + 1), the IAGO is used to establish the following grey model. xð0Þp ðkþ 1Þ ¼ xð0Þð1Þ b a e akð1 eaÞ ð12Þ and the predicted value of the primitive data at time (k + H): xð0Þp ðkþ HÞ ¼ xð0Þð1Þ b a e aðkþH 1Þð1 eaÞ: ð13Þ...

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  • ...Finally, using the predicted value, the Inverse Accumulating Generation Operator (IAGO) is applied to find the predicted values of original data....

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  • ...In order to smooth the randomness, the primitive data obtained from the system to form the GM(1,1) is subjected to an operator, named Accumulating Generation Operator (AGO) (Deng, 1989)....

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  • ...…; zð1ÞðnÞÞ; ð4Þ where zð1ÞðkÞ is the mean value of adjacent data, i.e. zð1ÞðkÞ ¼ 0:5xð1ÞðkÞ þ 0:5xð1Þðk 1Þ; k ¼ 2;3; . . . ;n: ð5Þ The least square estimate sequence of the grey difference equation of GM(1,1) is defined as follows (Deng, 1989): xð0ÞðkÞ þ azð1ÞðkÞ ¼ b: ð6Þ The whitening equation is…...

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Journal ArticleDOI
TL;DR: The relationships between intuitionistic fuzzy sets are established and interval-valued fuzzy sets, an extension of fuzzy set theory, are established.

710 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the stability and stabilization of a grey system whose state matrix is triangular is studied and the displacement operator and established transfer developed by the author are the indispensable tool for the grey system.

3,463 citations


"Introduction to Grey system theory" refers methods in this paper

  • ...Grey System theory was initiated in 1982 [7]....

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Book ChapterDOI
01 Jan 1987
TL;DR: The derivation of an irrigation strategy for the People’s Victory Channel is outlined, and experience of recent years proves that the effectiveness of this strategy is satisfactory.
Abstract: Using the concepts of a topological space and state, an approach to multitarget decision making — called grey decision making — has been developed. Some definitions and properties are given in this paper. As a successful example of grey decision making, the derivation of an irrigation strategy for the People’s Victory Channel is outlined. Experience of recent years proves that the effectiveness of this strategy is satisfactory.

5 citations

Journal Article
TL;DR: In this article, the existential theorem and the transfer function of the most economical controller by which the poles assignment for the given system may be obtained, are proposed, and the simplest structure and the least parameters controller to stabilize the given decentralized control system are studied.

3 citations

Journal Article
TL;DR: In this article, the problem of stability of grey linear time-invariant systems is investigated in virtue of the properiest of non-negative irreducible matrices, and the sufficient criterion for stability of gray linear time invariant systems are given, which is helpful to the analysis of the stability of line-time-varying systems as well as grey systems.
Abstract: In this paper the problem of stability of grey linear time-invariant systemsis investigated in virtue of the properiest of non-negative irreducible matrices.Besides,the sufficient criterion for stability of grey linear time-invariant systems aregiven.The criterion obtained here is helpful to the analysis of the stability of lineartime-varying systems as well as grey systems.As an illustrative example of the crite-rion,the sufficient condition is given under which the stability of linear time-varyingsystems is guaranteed.And in terms of the sufficient condition it is much more conve-nient and simpler to judge Whether some linear time-varying systm is stable or not.

1 citations