基于后悔理论的灰色随机多准则决策方法  

Method for grey-stochastic multi-criteria decision-making based on regret theory

作　　者：钱丽丽[1,2] 刘思峰[1] 方志耕[1] 刘勇[3] QIAN Li-li LIU Si-feng FANG Zhi-geng LIU Yong(College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China School of Business, Jiangnan University, Wuxi 214122, China)

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]上海立信会计金融学院统计与数学学院,上海201209 [3]江南大学商学院,江苏无锡214122

出　　处：《控制与决策》2017年第6期1069-1074,共6页Control and Decision

基　　金：国家自然科学基金项目(11101283;71503103);国家社科基金重点项目(12AZD102);欧盟第7研究框架玛丽居里国际人才引进计划Fellow项目(FP7-PIIF-GA-2013-629051);江苏自然科学基金项目(BK20150157);江苏社科基金项目(14GLC008)

摘　　要：针对准则值和状态概率均为区间灰数的灰色随机多准则决策问题,在考虑决策者的风险态度及心理行为的情境下,给出一种基于后悔理论的决策方法.首先将原始准则值转化为标准灰数,同时进行规范化处理,得到各状态下的标准灰色风险决策矩阵;然后依据后悔理论,定义灰色感知效用函数,构造决策者对方案集的灰色综合感知效用最大化的多目标优化模型,并解出最优权重向量,得到各方案的最优灰色感知效用值且排序;最后,通过实例验证所提出方法的可行性和有效性.In the situation of considering the decision-maker＇s risky attitude and psychological behavior, a decision analysis method based on the regret thoery is proposed to solve the problem of grey-stochastic multi-criteria decisionmaking in which the criteria value of alternatives and the probability are both grey numbers. Firstly, original criteria values are converted into standard grey numbers, and the standard grey risky decision matrix under various conditions is obtained by using the normative approach. Then, the grey perceived utility function is defined based on the regret thoery. A multi-objective optimization model which produces the maximum grey overall perceived utility values of alternatives is constrcted to get the optimum weight vector, so that the optimal grey perceived utility value of each scheme is ranked by the sorting rules of interval grey numbers. Finally, an example is provided to illustrate the practicability and effectiveness of the proposed method.

关 键 词：灰色随机 多准则决策 区间灰数 后悔理论 灰色感知效用 最优权重 

分 类 号：N941.5[自然科学总论—系统科学]