中文摘要：

依据惩罚型状态变权向量的定义和对各因素间的均衡性要求,构造了含有几何平均值的惩罚型状态变权向量.给出了各因素的几何平均值相等和几何平均值不相等两种情况的构造方法,对多因素的变权综合提供了有效的理论支持.最后,用一个实例验证了该方法 的可行性和有效性.

英文摘要：

The method of penalized state variable weight vector consisting of geometric mean in terms of the definition of penalized state variable weight vector and among equilibrium of the various factors is studied in this paper. The penalized state variable weight vectors of equal geometric mean and unequal geometric mean are given. This method provides effective theoretical support on the variable weight synthesis of multiple factors. Finally, the feasibility and effectiveness is verified by the numerical example.