The foundation of the grey matrix and the grey input-output analysis

Abstract The grey systems theory aims at the objects that their information is inadequate and this situation is general in reality. It has been urgent work to study the uncertain problems using the missing information. With the help of the simple introduction of grey systems theory, we further study the covered operation and get some calculation rules about grey number. The definition of grey matrix (GM) and its covered operation are proposed. Particularly, some results of the inverse grey matrix are obtained. Also with the help of the proposed grey matrix theory and the traditional input–output analysis, we propose the grey input–output analysis. The most important results are the computational formulas and their rigorous proofs of the matrix-covered set of the inverse grey Leontief coefficient’s matrix. It provides an effective tool to study an economic system by the input–output analysis under the uncertain situation. The modified case verifies the effectiveness of our methodology.

[1]  Barnett R. Parker,et al.  An application of organizational input-output analysis to hospital management , 2005 .

[2]  Yi Lin,et al.  An Introduction to Grey Systems: Foundations, Methodology and Applications , 2003 .

[3]  N. B. Chang,et al.  Grey input-output analysis and its application for environmental cost allocation , 2003, Eur. J. Oper. Res..

[4]  Masatake Nagai,et al.  A GM(1,1)–Markov chain combined model with an application to predict the number of Chinese international airlines , 2007 .

[5]  Yoshikuni Yoshida,et al.  Reliability of LCI considering the uncertainties of energy consumptions in input–output analyses , 2002 .

[6]  G. West,et al.  A Stochastic Analysis of an Input-Output Model , 1986 .

[7]  J. R. San Cristóbal,et al.  The mining industry in the European Union: Analysis of inter-industry linkages using input-output analysis , 2006 .

[8]  Manfred Lenzen,et al.  Environmental impact assessment including indirect effects—a case study using input–output analysis , 2003 .

[9]  Hyun-Sik Chung,et al.  Change in CO2 emission and its transmissions between Korea and Japan using international input–output analysis , 2006 .

[10]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[11]  Clark W. Bullard,et al.  Monte Carlo Sensitivity Analysis of Input-Output Models , 1988 .

[12]  V. Albino,et al.  Input–output models for the analysis of a local/global supply chain , 2002 .

[13]  Sangwon Suh,et al.  A note on the calculus for physical input–output analysis and its application to land appropriation of international trade activities , 2004 .

[14]  H. Breusers,et al.  Applied Mathematical Modelling , 1976 .

[15]  András Simonovits,et al.  A Note on the Underestimation and Overestimation of the Leontief Inverse , 1975 .

[16]  Hong Zhang,et al.  Application of grey modeling method to fitting and forecasting wear trend of marine diesel engines , 2003 .

[17]  Changzhi Yang,et al.  Grey model of direct solar radiation intensity on the horizontal plane for cooling loads calculation , 2000 .

[18]  Zhuguo Li,et al.  Grey target theory based equipment condition monitoring and wear mode recognition , 2006 .

[19]  Reiner Franke,et al.  Structural change in the manufacturing sector and its impact on business-related services: an input–output study for Germany , 2005 .

[20]  J. Singh,et al.  Application of Grey System Theory in the Development of a Runoff Prediction Model , 2005 .

[21]  O. Karkacıer,et al.  Input–output analysis of energy use in agriculture , 2005 .

[22]  Ni-Bin Chang,et al.  Corporate optimal production planning with varying environmental costs: A grey compromise programming approach , 2004, Eur. J. Oper. Res..

[23]  Zhao Xiu.  Input-output Models and Prediction of Uncertain Economic System , 2001 .

[24]  David K. W. Ng,et al.  Contrasting grey system theory to probability and fuzzy , 1995, SICE.

[25]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[26]  Victor R. L. Shen,et al.  A novel cryptosystem based on grey system theory and genetic algorithm , 2005, Appl. Math. Comput..

[27]  Thijs ten Raa.  The Economics of Input-Output Analysis: The dynamic inverse , 2006 .

[28]  B. W. Ang,et al.  A trigonometric grey prediction approach to forecasting electricity demand , 2006 .