Research On The Grey Input-output Analysis And The Extensive Adjustment Of Direct Consumption Coefficient

The grey systems theory and the extenics are new subjects which are all originated by Chinese scholars. The researching objective of grey systems theory is the uncertain system whose information is partly knowable and partly unknowable. Its character is missing information. We can find its regularity using the knowable information. The extenics utilizes the formalized model to explore the extensive probability of objects, and we can get their regularity and obtain some methods to resolve the incompatible problems. The extenics studies the object's transformation through the qualitative analysis and the quantitative one, then the incompatible problems can be resolved.The input-output analysis reflects the dependent relationship between the input and the output of an economic system's sectors. It is generally applied in economic analysis, policy simulation, economic forecasting and system's controlling, etc.. The successfully application is greatly dependent on the accuracy of direct consumption coefficients.Because the information about the economic system is missing, and it is incompatible between the hypothetic conditions about the direct consumption coefficients and the inquiry to correctly reflect the actual economy, we propose the grey input-output analysis and the extensive adjustment of direct consumption coefficient. The innovative aspects are below:(1) We describe the conception and connotation of grey number in detail, and proposed the foundation of grey matrix theory and grey function. Then the basic structure of grey mathematics is founded. The exciting results are the computational method of inverse grey matrix and the operational rules of grey element, which are essential for grey systems theory.(2) The generally elementary dependent functions are constructed, which include the certain and uncertain types. The functions describe not only the variable degree of the object, but also its trend. They can show the general regularity of the actual object's transformation and have more applied fields.(3) With the help of grey matrix theory, we propose the grey input-output analysis. The results include the national value-type grey static input-output analysis, grey dynamic one, grey enterprise one, grey input-occupancy-output analysis and grey non-linear one, etc.. The covered sets of inverse grey coefficient matrix for every type of grey models are obtained.(4) The extensive adjustment of direct consumption coefficient is proposed. It is based on the characteristic that the generally elementary dependent function can describe the degree and tend of the object's variation. This approach can make the adjustment be more easily and let the output structure be the optimal one, so the economic system keeps balance.