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针对准则值为扩展灰数形式的风险型多准则决策问题,提出一种基于扩展灰数Hausdorff距离的随机多准则决策方法.首先定义了离散型扩展灰色随机变量及期望值和标准差,并在Hausdorff距离的基础上提出了扩展灰数的Hausdorff距离公式;然后计算每个方案在各准则下的期望值,得到期望值决策矩阵;再根据传统TOPSIS方法的思想,提出一种基于TOPSIS的灰色随机多准则决策方法.最后,通过实例验证了所提出方法的合理性和可行性.
Aiming at the risk-based multi-criteria decision problem whose criterion value is an extended gray number, a stochastic multi-criteria decision-making method based on extended gray number Hausdorff distance is proposed. First, the discrete extended gray random variables and their expected values and standard deviations are defined, Then the Hausdorff distance formula of extended gray numbers is proposed based on the distance and the distance between them. Then the expected value under each criterion is calculated to get the expected value decision matrix. Then according to the traditional TOPSIS method, a gray stochastic multi-criteria decision-making method based on TOPSIS Finally, an example is given to verify the rationality and feasibility of the proposed method.