基于改进调节变量主成分权重的广义灰靶决策模型研究

在现实生活中，由于信息的不完全性和认知的不充分性，多数决策对象具有强烈的多源不确定性特点，存在多种不确定性因素共存的现象.针对目前灰靶决策模型未充分考虑决策对象多种不确定性因素共存的局限，以及确定决策指标权重时未深入探讨指标间相关性的问题，首先引入广义灰数的表征形式对指标属性值进行统一表征，并提出广义灰数的一致效果测度模型，然后根据传统主成分分析法确定权重时所存在的二次加权放大问题，揭示指标差异性与相关性对二次加权的影响，通过改进调节变量对原始主成分权重进行修正，接着将传统的灰靶决策模型扩展为广义灰数形式，构建基于加权欧式距离的广义灰靶靶心距模型，并据此建立基于改进调节变量主成分权重的广义灰靶决策模型.最后通过案例研究，验证本文模型的合理性和可行性.

Research on generalized grey target decision model based on principal component weight of improved regulating variables

Due to the incompleteness of information and the insufficiency of cognition, most decision-makings have strong multi-source and uncertainty characteristics, which causes many uncertain factors coexist. At present, the grey target decision model doesn't adequately consider the limitations of multiple uncertain factors' coexistence in decision-making objects, and doesn't deeply discuss the correlation between indicators when determining the weight of decision indicators. To solve these problems, firstly, we apply generalized grey number to simultaneously characterize multiple attribute data of indicators. At the same time, we define a consistent effect measure model for generalized gray numbers. Then, reveal the impact of indicator differences and correlations on secondary weighting, since traditional principal component analysis (PCA) has a problem to absorb twice information. And correct the original PCA weights by improving the regulating variables. Next, construct the off-target distance model based on weighted Euclidean distance with extending to a generalized gray number form. Therefore, a generalized grey target decision model based on principal component weight of improved regulating variables is proposed. Finally, through a case study, we prove the rationality and feasibility of the model.