一种基于前景理论的灰色多属性风险型决策方法

A Method for Grey Multi-attribute Risk Decision-making Based on Prospect Theory

针对属性权重完全未知且属性值为区间灰数的多属性风险型决策问题,提出了一种基于前景理论的决策方法.首先将原始风险决策矩阵标准化,并以此构造正、负理想方案,根据各方案与正、负理想方案的关联系数,利用离差最大化优化模型求解属性权重;然后在前景理论和灰色关联分析方法的基础上构建前景价值函数和权重函数,进而依据各方案综合前景值的大小确定出方案的优劣排序.最后通过一个实例说明了该算法的可行性和有效性.

For the problem of multi-attribute risk decision-making with interval grey numbers attribute values and unknown attribute weights, a method is proposed based on the prospect theory. Firstly, the original risk decision-making matrix is standardized, and then the positive and negative ideal schemes are obtained. According to the correlation coefficient between the alternative and the positive and negative ideal schemes, the attribute weight is solved by using the maximum deviation optimization model. Secondly, on the basis of the prospect theory and grey relational analysis, the prospect value function and the prospect weight function are constructed. Furthermore, the order of alternatives can be listed by comparing the comprehensive prospect value of each alternative. Finally, the feasibility and effectiveness of the algorithm is validated by an example.