基于加权平均量的自收敛性的权的确定理论

【作者】 徐东胜；

【导师】 李小明；

【作者基本信息】 西南石油大学 ， 应用数学， 2006， 硕士

【摘要】 综合评价理论的理论、方法在管理科学与工程领域中占有重要的地位，已成为经济管理、工业工程及决策等领域中不可缺少的重要内容，且有着重大的实用价值和广泛的应用前景。对于有限多个方案的决策问题来说，没有科学的综合评价，就没有正确的决策。而综合评价问题的核心，是权重系数的确定。 如何确定权重系数?目前，国内外按照其适用原理分为这样三类：第一类是基于“功能驱动”原理的赋权法；第二类是基于“差异驱动”原理的赋权法；第三类是综合集成赋权法。基本上对应我们通常说的主观赋权法、客观赋权法和主客观结合赋权法。 但是主观评价透明性、可再现性差，客观方法又缺乏理论基础，主客观结合赋权法也往往不注重理论。于是，我们提出了加权平均量的自收敛性这一概念，从概率论基础入手，应用Lagrange乘积因子法，得到了一般情况下权重系数确定的优化模型、协方差矩阵为正定矩阵和影响因子相互独立时的一系列的确定权数的理论，建立了一套较完整的确定权重系数的方法的理论，使赋权理论这种方法向成熟化靠近了一步。 最后，针对高校教师课堂教学质量评价问题，我们应用我们提出的这个理论进行了求解，给出了比较合理实用的结果，并与目前比较流行的方法——层次分析法，进行了比较和结合。自收敛法在进行两两比较上提供了有效的武器——方差的大小不同，如果以此为基础，则也可以解决层次分析法含有主观色彩，评价过程的透明性、可再现性差的弱点。更多还原

【Abstract】 The theory and approach of the comprehensive evaluation theory has taken an important place in management science and project. It also has become an indispensable part in the fields such as economic management, industrial project and decision, and has crucial practical value and good prospect to apply. To the decision with finite programs, comprehensive evaluation is the premise of decision. There is no right decision without scientific comprehensive evaluation. However the decision to Weight is the core of comprehensive evaluation.But how to decide weight? Currently, in terms of its applied principle, three categories have been made at home or overseas: the first category is based on Weight decision of the principle of function drive; the second category is based on Weight decision of the principle of difference drive; the third category is synthetic Weight. Generally speaking, the three categories are equal to Subjective Weight, Objective Weight, Subjective and Objective Weight. But subjective evaluation has poor transparency and reappearance, objective method lacks of theoretical foundation, subjective and objective Weight tends to pay no attention to theory. To deal with the situation talked above, we put forth the new concept of "the auto-convergence of weighed average". Beginning with the basic conceptualism, by the law of Lagrange probability, we have had an optimizing mode to decide Weight in general condition an, a series of Weight theory of covariance matrix being positive matrix, and Factors affecting mutual independence weight factor determining, had set up a suit of full method and theory to decide Weight, putting a further step to mature.At last, to the teaching problems made by teachers in classroom in everyday life, we apply the theory put forward by us to solve it and give the applied result. We also compare the analytic hierarchy process, which are popular currently. With the ’unique weapons ’—covariance matrix different size, we may get a solution to contain subjective color, transparency in the evaluation process, to the reappearance of poor weaknesses.更多还原