基于改进前景理论的直觉模糊随机多准则决策方法
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摘要
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.
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.
引文
[1]Atanassov K.lntuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
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[3]Chen S M,Tan J M.Handling multi-criteria fuzzy decision-making problems based on vague set theory[J]Fuzzy Sets and Systems,1994,67(2):163-172.
[4]Hong D H,Choi C H.Multi-criteria fuzzy decisionmaking problems based on vague set theory[J].Fuzzy Sets and Systems,2000,114(1):103-113.
[5]高建伟,刘慧晖,谷云东.基于前景理论的区间直觉模糊多准则决策方法[J].系统工程理论与实践,201434(12):3175-3181.(Gao J W,Liu H H,Gu Y D.Interval-valued intuitionistic fuzzy multi-criteria decision-making methods based on prospect theory[J].Systems Engineering-Theory&Practice,2014,34(12):3175-3181.)
[6]Ye J.Improved method of multi-criteria fuzzy decisionmaking based on vague sets[J].Computer-Aided Design2007,39(2):164-169.
[7]吴冲,刘千,万翔宇.基于改进得分函数的直觉模糊多属性决策方法[J].统计与信息论坛,2014,29(1):3-8.(Wu C,Liu Q,Wan X Y.Intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function[J].Statistics&Information Forum,2014,29(1):3-8.)
[8]王坚强,李婧婧.基于记分函数的直觉随机多准则决策方法[J].控制与决策,2010,25(9):1297-1306.(Wang J Q,Li J J.Intuitionistic random multi-criteria decision-making approach based on score functions[J].Control and Decision,2010,25(9):1297-1306.)
[9]Kahneman D,Tversky A.Prospect theory:An analysis of decision under risk[J].Econometrica,1979,47(2):263-291.
[10]王坚强,孙腾,陈晓红.基于前景理论的信息不完全的模糊多准则决策方法[J].控制与决策,2009,24(8):1198-1202.(Wang J Q,Sun T,Chen X H.Multi-criteria fuzzy decision-making method based on prospect theory with incomplete information[J].Control and Decision,2009,24(8):1198-1202.)
[11]马健,孙秀霞.基于效用曲线改进的前景理论价值函数[J].信息与控制,2011,40(4):501-506.(Ma J,Sun X X.Modified value function in prospect theory based on utility curve[J].Information and Control,2011,40(4):501-506.)
[12]Bernoulli D.Exposition of a new theory on the measurement of risk[J].Econometrica,1954,22(1):22-36.
[13]Fullér R,Majlender P.On obtaining minimal variability OWA operator weights[J].Fuzzy Sets and Systems,2003,136(2):203-215.
[14]Wang Y M,Luo Y,Liu X W.Two new models for determining OWA operator weights[J].Computers&Industrial Engineering,2007,52(2):203-209.
[15]Yari G,Chaji A R.Maximum Bayesian entropy method for determining ordered weighted averaging operator weights[J].Computers&Industrial Engineering,2012,63(1):338-342.
[2]Zadeh L A.Fuzzy sets[J].Information and Control,19658(3):338-353.
[3]Chen S M,Tan J M.Handling multi-criteria fuzzy decision-making problems based on vague set theory[J]Fuzzy Sets and Systems,1994,67(2):163-172.
[4]Hong D H,Choi C H.Multi-criteria fuzzy decisionmaking problems based on vague set theory[J].Fuzzy Sets and Systems,2000,114(1):103-113.
[5]高建伟,刘慧晖,谷云东.基于前景理论的区间直觉模糊多准则决策方法[J].系统工程理论与实践,201434(12):3175-3181.(Gao J W,Liu H H,Gu Y D.Interval-valued intuitionistic fuzzy multi-criteria decision-making methods based on prospect theory[J].Systems Engineering-Theory&Practice,2014,34(12):3175-3181.)
[6]Ye J.Improved method of multi-criteria fuzzy decisionmaking based on vague sets[J].Computer-Aided Design2007,39(2):164-169.
[7]吴冲,刘千,万翔宇.基于改进得分函数的直觉模糊多属性决策方法[J].统计与信息论坛,2014,29(1):3-8.(Wu C,Liu Q,Wan X Y.Intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function[J].Statistics&Information Forum,2014,29(1):3-8.)
[8]王坚强,李婧婧.基于记分函数的直觉随机多准则决策方法[J].控制与决策,2010,25(9):1297-1306.(Wang J Q,Li J J.Intuitionistic random multi-criteria decision-making approach based on score functions[J].Control and Decision,2010,25(9):1297-1306.)
[9]Kahneman D,Tversky A.Prospect theory:An analysis of decision under risk[J].Econometrica,1979,47(2):263-291.
[10]王坚强,孙腾,陈晓红.基于前景理论的信息不完全的模糊多准则决策方法[J].控制与决策,2009,24(8):1198-1202.(Wang J Q,Sun T,Chen X H.Multi-criteria fuzzy decision-making method based on prospect theory with incomplete information[J].Control and Decision,2009,24(8):1198-1202.)
[11]马健,孙秀霞.基于效用曲线改进的前景理论价值函数[J].信息与控制,2011,40(4):501-506.(Ma J,Sun X X.Modified value function in prospect theory based on utility curve[J].Information and Control,2011,40(4):501-506.)
[12]Bernoulli D.Exposition of a new theory on the measurement of risk[J].Econometrica,1954,22(1):22-36.
[13]Fullér R,Majlender P.On obtaining minimal variability OWA operator weights[J].Fuzzy Sets and Systems,2003,136(2):203-215.
[14]Wang Y M,Luo Y,Liu X W.Two new models for determining OWA operator weights[J].Computers&Industrial Engineering,2007,52(2):203-209.
[15]Yari G,Chaji A R.Maximum Bayesian entropy method for determining ordered weighted averaging operator weights[J].Computers&Industrial Engineering,2012,63(1):338-342.