基于扩展灰数Hausdorff距离的随机多准则决策方法

Stochastic multi-criteria decision-making method based on Hausdorff distance of extended grey numbers

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.

For the risk multi-criteria decision-making problems in which the criteria value of alternatives are in the form of extended grey numbers, a grey stochastic multi-criteria decision-making approach is proposed based on the Hausdorff distance of extended grey numbers. Firstly, the discrete extended grey random variable as well as its expected value and standard deviation are defined. Then, motivated by the idea of the Hausdorff distance, the Hansdorff distance of extended grey numbers is defined. The expected value of each alternative under every criterion is calculated, and then the expected valued decision matrix is obtained. After that, a TOPSIS-based grey stochastic multi-criteria decision-making approach is built according to the idea of traditional TOPSIS method. Finally, an example is given to verify the effectiveness and feasibility of the developed approach.