三参数区间灰数信息下风险型多准则决策方法

针对概率和准则值均为三参数区间灰数的多准则决 策问题,本文提出了一种基于前景理论的决策方法. 该方法首先定义了三参数区间灰数的距离和精确记分函数,并通 过讨论其性质给出了比较大小的方法; 其次,通过给出三参数区间灰数前景价值和概率权重函 数的定义,以多参考点为思路,构建前景决策矩阵, 并通过提出参考点集结算子,集结出综合前景决策矩阵. 进而,由优化模型求得的最优准则权系数加权得出方案的综合前景值及排序; 最后,通过算例对比说明了该方法的合理性和可靠性.

A Risky Multi-criteria Decision-making Method with Three-parameter Interval Grey Number

In view of the multi-criteria decision-making problem that probabilities and the criteria values of alternatives are both three-parameter interval grey number, a risky decision-making approach based on prospect theory is proposed. In this method, firstly, the distance and the exact function of three-parameter interval grey number are defined, and on the basis of the analysis and discussion of its properties, a three-parameter interval grey number comparison method is defined. Secondly, we give the definition of the prospect value function and the probabilities weighting function of three-parameter interval grey number. Then, the prospect value of each alternative is calculated based on multi-reference point, and the integrated prospect decision matrix is constructed by giving the reference point aggregating operator. Moreover, the integrated prospect value of each alternative is aggregated by the integrated prospect decision matrix and the optimal criteria weights given by the optimization model. After that we can order these alternatives by comparing their integrated prospect values. Finally, an example is presented to examine the effectiveness of our method.