一种基于前景理论和改进TOPSIS的模糊随机多准则决策方法及其应用

Method for Fuzzy-stochastic Multi-criteria Decision-making Based on Prospect Theory and Improved TOPSIS with its Application

针对准则值为区间灰数直觉模糊数、准则权系数部分已知以及自然状态出现概率为灰数的多准则决策问题,提出一种结合前景理论和改进TOPSIS的决策方法。该方法首先定义了灰色直觉模糊数的前景价值函数和概率权重函数,并利用前景理论构建出前景决策矩阵;接着从两个方面对传统TOPSIS决策方法进行改进:(1)过定义方案间综合差异的概念,采用离差最大化思想,建立平均综合差异最大化规划模型,给出了一种兼顾主客观权重信息确定准则权系数的新方法;(2)用灰关联替换备选方案与正负理想方案的距离,据此刻画了各方案与正负理想方案的贴近度。进而利用改进TOPSIS决策方法中的综合贴近度对方案进行了排序。最后通过实例验证了该方法的有效性。

This paper investigates the grey-probability multi-criteria decision-making problem in which the criteria value is interval grey-intuitionistic fuzzy number and the weighted coefficients are partially known. A decisionmaking approach based on improved TOPSIS and Prospect theory is proposed. This approach is composed of two steps： the first one is defining prospect value function and probability weighting function of grey intuitionistic fuzzy numbers and constructing prospects decision matrix via prospect theory,and the second one is ordering the corresponding alternatives by applying the complex closeness degree of the improved TOPSIS method. As for the TOPSIS we improve it in two aspects： On the one hand,we first define the concept of the difference between alternatives,and consequently construct a maximum average difference program model by using the idea of maximizing deviations,and then,a calculating weight method which satisfies the manager subjective information with the algorithm of maximum deviation is proposed. On the other hand,we use the degree of grey relational instead of applying the distance of positive-negative ideal solution to measure the closeness degree of distance between alternatives and positive-negative ideal solution. Finally,an example is provided to examine the effectiveness of our method.