基于后悔理论的概率犹豫模糊双边匹配决策方法

针对概率犹豫模糊信息下准则具有期望水平的双边匹配决策问题,考虑双边主体后悔规避的心理行为特征,提出一种基于后悔理论的双边匹配决策方法.首先,定义概率犹豫模糊元的新兰氏距离和兰氏记分函数.然后,基于后悔理论提出一种准则具有期望水平的概率犹豫模糊双边匹配决策方法.该方法利用期望效用函数和概率犹豫模糊元兰氏记分函数构建双边主体的准则效用值矩阵;利用后悔-欣喜函数构建双边主体对于准则期望水平的后悔-欣喜值矩阵;依据后悔理论构建双边主体对于准则期望水平的感知价值矩阵.进一步,先利用离差最大化思想和概率犹豫模糊元新兰氏距离构建优化模型求解准则权重,再利用线性加权法构建双边主体的综合感知价值矩阵,利用极差变换法构建双边主体的满意度矩阵.在此基础上,基于满意度最大化,构建考虑双边匹配方案稳定性的多目标优化模型,并通过求解模型得到双边匹配结果.最后,通过算例分析表明了所提出匹配决策方法的有效性和实用性.

Two-sided matching decision making method with probabilistic hesitant fuzzy information based on regret theory

With respect to the probabilistic hesitant fuzzy two-sided matching decision making problems with aspiration levels on criteria, a two-sided matching decision making method based on the regret theory is proposed considering the psychological behaviour of regret aversion of two-sided matching subjects. Firstly, a new Lance distance measure and a Lance score function of the probabilistic hesitant fuzzy element are defined. Then, based on the regret theory, a probabilistic hesitant fuzzy two-sided matching decision making method with aspiration levels on criteria is proposed. In this method, the criterion utility value matrix of two-sided matching subjects are constructed using the expected utility function and the Lance score function of the probabilistic hesitant fuzzy element, the regret-rejoice value matrix of two-sided matching subjects relative to the aspiration levels on criteria are built using the regret-rejoice function, and the perceived value matrix of two-sided matching subjects relative to the aspiration levels on criteria are set up according to the regret theory. Furthermore, an optimization model is constructed using the ideas of maximal deviation method and the new Lance distance measure of the probabilistic hesitant fuzzy element to obtain the weight vectors of the criteria, the comprehensive perceived value matrix of two-sided matching subjects are built using the linear weighted method, and the satisfaction degree matrix of two-sided matching subjects are set up using the range transformation method. Based on these, a multi-objective optimization model is constructed considering maximal satisfaction degree and the stability of two-sided matching alternatives, and the stable two-sided matching outcomes are obtained by solving this model. Finally, an example is given to illustrate the effectiveness and practicability of the proposed two-sided matching decision making method.