【作者】 李桥兴；

【导师】 刘思峰；

【作者基本信息】 南京航空航天大学 ， 管理科学与工程， 2007， 博士

【摘要】 灰色系统理论和可拓学都是由我国学者创立的学科。灰色系统理论研究“部分信息已知、部分信息未知”的不确定性系统,把具有贫信息特征的事物作为研究对象,利用部分已知信息去发现和认识事物的发展规律。可拓学是采用形式化模型研究事物拓展的可能性和开拓创新的规律与方法,并用于解决矛盾问题的科学。矛盾是事物发展的动力。可拓学从定性和定量相结合的角度研究事物的变化,帮助人们处理矛盾问题。投入产出分析反映经济系统各部分之间的投入与产出的数量依存关系,并广泛应用于经济分析、政策模拟、经济预测、计划制定和经济控制等的数量分析方法。投入产出分析的价值和意义在很大程度取决于直接消耗系数的准确性。根据经济系统的贫信息特征,以及直接消耗系数的假设条件与要求正确反映现实经济系统之间的矛盾,提出灰色投入产出分析基础和直接消耗系数的可拓调整方法。本文的主要创新点概括为以下几个方面:(1)详细阐述了灰数的概念和内涵,提出灰矩阵理论基础和灰色函数的基本概念体系,构建灰色数学基本框架。重新阐述灰数的概念和内涵;结合矩阵知识,建立灰色矩阵理论基础,特别是提出逆灰矩阵的定义及运算方法;结合实函数的基本知识,提出灰色函数的基本概念体系;在此基础上,提出灰色系统理论运算的基本概念——灰元运算,从而具备了灰色数学的基本雏形。(2)构造确定性和非确定性的一般初等关联函数。通过构造一般初等关联函数,使关联函数不但可以描述事物发生质变和量变的程度,而且体现了变化趋势的强弱,能说明事物变化的一般规律,有更广的适用范围。(3)在灰色矩阵理论基础上,提出较完整的灰色投入产出分析基础。本文取得的主要研究成果包括:全国价值型灰色静态投入产出分析、灰色动态投入产出分析、灰色企业投入产出分析、灰色投入占用产出分析和灰色非线性投入产出分析等,并给出了各种灰色模型的灰色系数矩阵的逆灰矩阵的覆盖解。(4)提出直接消耗系数的可拓调整方法。利用一般初等关联函数能够描述事物变化的程度和趋势等特点,对直接消耗系数进行修订。该方法可以使系数的调整相对容易可行,而且对应的产出结构为最优产出结构,使经济系统能够保持平衡协调发展。更多还原

【Abstract】 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.更多还原