基于改进前景理论的直觉模糊随机多准则决策方法

Intuitionistic fuzzy stochastic multi-criteria decision-making method based on modified prospect theory

针对方案准则值为直觉模糊数、准则权重信息部分已知的随机多准则决策问题,提出一种基于改进前景理论的决策分析方法.首先,定义一个新的记分函数,据此可将直觉模糊数转化为实数.其次,考虑到决策者并非完全理性及决策者风险态度的差异性,将决策者分为保守型、中间型及冒险型,引入改进前景理论,根据不同决策者类型调整参数,构建改进前景决策矩阵.再次,建立以准则值总差异最大化且准则权重差异最小化为目标的非线性二次偏差优化定权模型,计算准则权重.进而,结合改进前景决策矩阵及准则权重计算各方案的综合效用值,并以此确定方案的顺序排列.最后,通过算例验证所提出直觉模糊随机多准则决策方法的有效性和合理性.

This paper provides an approach based on the modified prospect theory solving the intuitionistic fuzzy stochastic multi-criteria decision-making problem where the information of criteria weights is partially known. Firstly, a new score function is defined, by which the intuitionistic fuzzy numbers can be transformed into the real numbers. Then,considering that decision-makers are not completely rational and there are differences among them, the types of decisionmakers attitudes towards risk can be classified into risk-seeking, risk-neutral and risk-averse. The modified prospect value decision-making matrix is constructed by applying the modified prospect theory and adjusting its parameters to fit different types of decision-makers. In addition, a nonlinear quadratic deviation optimization model is established,whose goal is maximizing the total difference of criteria values and at the same time minimizing the difference between criteria weights. Furthermore, the order of alternatives is listed on the basis of the integrated utility values, which are derived by the modified prospect decision-making matrix and criteria weights. Finally, an example is given to illustrate the effectiveness and rationality of the proposed method.