风险型多属性决策的一种求解方法

在属性取值的分布函数已知的假设条件下,给出了风险型多属性决策问题的一种求解方法.通过随机变量取值大小的比较,利用概率指标描述方案在同一属性下的优劣程度;基于加权的思想,将方案在各属性下的优劣程度集结得到方案间的总体优劣程度,并建立方案两两比较的可能度矩阵——模糊互补判断矩阵.据此得到方案的排序结果.该方法直观、简便,而且不要求对风险决策矩阵进行规范化.最后,把属性值为区间数的多属性决策问题作为风险型多属性决策问题的特例,给出了算例.

Method for solving multi-attribute decision-making problems with risk

Multiattribute decision problems with uncertainty largely exist in the real world. A method for solving stochastic multiattribute decision problems was presented. Assuming that the performance probability density function for each alternative on each attribute was known, the probability that one random variable was greater than another employed in comparing evaluation of alternatives with respect to attributes. According to the concept of weighting, the local preferences were aggregated to build global preference relationship between each alternative pair. Owing to this, a fuzzy complementary judgment matrix, called pos- sibility degree matrix, was obtained. The ranking of the alternatives could be constructed from the matrix. The new method is intuitionistic and simple. And there was no need of normalization of the decision matrix.At last, the method was illustrated by multiattribute decision problems whose evaluations of alternatives were expressed by interval numbers.