基于期望值的灰色随机多准则决策方法

Grey random multi-criteria decision-making approach based on expected value

定义了离散型灰色随机变量及其期望值和标准差.针对准则权重已知而方案的准则值为灰色随机变量的多准则问题,提出一种灰色随机多准则决策方法.该方法通过求得各方案在各准则下评价值的期望值和标准差,得到标准期望值决策矩阵;利用各准则权重和规范化矩阵计算出各方案的综合评价区间,采用区间灰数可能度的方法构建方案综合评价区间的评判矩阵,进而得到各方案的排序.最后通过算例表明了该方法的可行性和有效性.

In this paper, discrete grey random variable as well as its expected value and standard deviation are defined. As for the multi-criteria decision-making problems, in which the criteria weights are completely known and the criteria value of alternatives are in the form of grey random variables, a grey random multi-criteria decision-making approach is proposed. In the method, the expected value and the standard deviation of each alternative under every criterions are gained separately firstly. After that, a standard expected value decision-making matrix can be formed. And the range of comprehensive evaluation for each alternative can be attained by the matrix operation between the vector of criteria weights and the normalizing decision-making matrix. By using the calculation method of probability degree of interval grey numbers, the evaluation matrix of the range of comprehensive evaluation for alternatives can be enacted and the order of the alternatives can be listed. Finally, an example shows the feasibility and validity of this approach.