基于前景理论的改进灰色关联多属性群决策方法

An improved grey relational multi-attribute group decision-making method based on prospect theory

针对属性指标权重未知、决策者权重已知,且属性值为区间二元语义变量的多属性群决策问题,提出了一种基于前景理论的改进灰色关联分析方法.首先,根据区间二元语义变量之间的广义距离对灰色关联度公式进行了改进,并定义了基于改进灰色关联度的前景价值函数;其次,构建了方案综合前景值最大化的非线性规划模型,并通过模型的最优权重确定各方案的排序;最后,通过数值模拟说明了该方法的有效性和可行性.

An improved grey relational analysis method based on the prospect theory is proposed to solve the multi-attribute group decision-making problem in which the weights of attributes are unknown,the weights of decision-makers are known,and the attribute values are interval-valued 2-tuple linguistic variables.Firstly,the grey relational degree formula is improved according to the generalized distance between the interval-valued 2-tuple linguistic variables,and the prospect value function is redefined based on the improved grey relational degree.Secondly,a nonlinear programming model is constructed to maximize the comprehensive prospect value of alternatives,and the optimal weights of the model are used to determine the ranking of the alternatives.Finally,the effectiveness and feasibility of the method are illustrated by numerical simulation.