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Grey enterprise input-output analysis. (English) Zbl 1237.93101

Summary: A system whose information is partially known and partially unknown to the investigator is named a grey system. Due to various inevitable noises contained in the process of data collection, managers of enterprise usually have to deal with poor information and make decisions under the influence of uncertainty. In this article, we propose grey enterprise input–output analysis. The value and the physical types of grey models are established. In particular, we present a detailed way of calculating the matrix-covered set of the inverse of a grey triangular matrix. The proposed method makes the management of enterprises more practically possible when the available data contains uncertainty. At the end, we look at a case study to show the practical feasibility of our work.

MSC:

93C41 Control/observation systems with incomplete information
93B30 System identification
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References:

[1] Deng, J., The control problems of grey systems, Systems and Control Letters, 5, 288-294 (1982) · Zbl 0482.93003
[2] Li, Q.; Liu, S., The foundation of the grey matrix and the grey input-output analysis, Applied Mathematical Modelling, 32, 3, 267-291 (2008) · Zbl 1141.93036
[3] Deng, J., Greyness and uncertainty of grey system, The Journal of Grey System, 3, 236 (1995)
[4] Q.X. Li, Research on the grey input-output analysis and the extensive adjustment of direct consumption coefficient, Ph.D. Thesis, Nanjing University of Aeronautics and Astronautics, Nanjing, 2007 (in Chinese).; Q.X. Li, Research on the grey input-output analysis and the extensive adjustment of direct consumption coefficient, Ph.D. Thesis, Nanjing University of Aeronautics and Astronautics, Nanjing, 2007 (in Chinese).
[5] Li, Q., The grey elementary functions and their grey derived functions, The Journal of Grey System, 20, 3, 245-254 (2008)
[6] Li, Q.; Liu, S., Some results about grey mathematics, Kybernetes, 38, 3-4, 297-305 (2009) · Zbl 1197.93017
[7] Chang, N.; Wu, C., Corporate optimal production planning with varying environmental costs: a grey compromise programming approach, European Journal of Operational Research, 155, 68-95 (2004) · Zbl 1045.90025
[8] Chen, S.; Li, Z.; Xu, Q., Grey target theory based equipment condition monitoring and wear mode recognition, Wear, 260, 438-449 (2006)
[9] Chen, T.; Shai, K.; Shen, V., A novel cryptosystem based on grey system theory and genetic algorithm, Applied Mathematics and Computation, 170, 1290-1302 (2005) · Zbl 1083.94010
[10] Huang, G.; Baetz, B.; Patry, G., Grey integer programming: an application to waste management planning under uncertainty, European Journal of Operational Research, 83, 594-620 (1995) · Zbl 0899.90131
[11] Li, Q., The covered solution of grey linear programming, The Journal of Grey System, 4, 309-320 (2007)
[12] Li, Q. X., Grey dynamic input-output analysis, Journal of Mathematical Analysis and Applications, 359, 514-526 (2009) · Zbl 1172.91010
[13] Li, Q.; Liu, S., The grey input-occupancy-output analysis, Kybernetes, 38, 3-4, 306-313 (2009) · Zbl 1197.93018
[14] Liang, R., Application of grey linear programming to short-term hydro scheduling, Electric Power Systems Research, 41, 159-165 (1997)
[15] Li, Q.; Yang, J., The grey complex networks and design of some topological indexes of grey indirect networks, International Journal of Nonlinear Sciences, 5, 1, 33-38 (2008) · Zbl 1394.68016
[16] Lin, Y.; Lee, P. C.; Ting, H., Dynamic multi-attribute decision making model with grey number evaluations, Expert Systems with Applications, 35, 1638-1644 (2008)
[17] Trivedi, H.; Singh, J., Application of grey system theory in the development of a runoff prediction model, Biosystems Engineering, 92, 521-526 (2005)
[18] Albino, V.; Silvana, K., Enterprise input-output model for local sustainable development—the case of a tiles manufacturer in Italy, Resources, Conservation and Recycling, 41, 165-176 (2004)
[19] Kwak, S.; Han, S.; Yoo, S., The role of the four electric power sectors in the Korean national economy: an input-output analysis, Energy Policy, 32, 1531-1543 (2004)
[20] Li, Qiao-Xing, The grey departmental input-output analysis, The Journal of Grey System, 23, 1, 101-112 (2011)
[21] Horn, R.; Johnson, C., Topics in Matrix Analysis (1991), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0729.15001
[22] Jennings, A.; McKeown, J., Matrix Computations (1992), John Wiley and Sons: John Wiley and Sons New York · Zbl 0808.65015
[23] Johnson, L.; Riess, R.; Arnold, J., Introduction to Linear Algebra (2000), Prentice-Hall: Prentice-Hall New York
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