基于前景理论的三参数区间灰数信息下多属性灰关联决策方法
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摘要
针对决策信息为三参数区间灰数的多属性决策问题,考虑决策者主观风险态度,提出了一种基于前景理论的灰关联决策方法.首先,利用"奖优罚劣"的线性变换算子对原始决策信息进行规范化处理;其次,通过定义三参数区间灰数的相对核来判断其大小,将其融入前景理论给出前景价值函数和权重函数,由此确定正、负理想方案;然后,根据灰关联分析法得到正、负关联系数,进而确定综合相对贴近度实现对方案的排序;最后,由一个实例表明了所提方法的有效性和合理性.
Considering the subjective risk attitude of decision makers,a grey incidence decision method based on th e prospect theory is proposed for multi-attribute decision-making problems,in which the attribute value of alternatives is three-parameter internal grey number.Firstly,the linear transformation operator of "rewarding good and punishing bad" is used to normalize the original decision-making information.Then,the relative kernel is defined to determine the size of three-parameter interval grey number,and the prospect value function and the weight function are given based on the relative kernel and prospect theory,which can determined the positive and negative ideal schemes.Next,the positive and negative incidence coefficients are given based on the grey relational analysis,and then the comprehensive close degree is determined to sort the schemes.Finally,an example is presented to illustrate the validity and rationality of the proposed method.
Considering the subjective risk attitude of decision makers,a grey incidence decision method based on th e prospect theory is proposed for multi-attribute decision-making problems,in which the attribute value of alternatives is three-parameter internal grey number.Firstly,the linear transformation operator of "rewarding good and punishing bad" is used to normalize the original decision-making information.Then,the relative kernel is defined to determine the size of three-parameter interval grey number,and the prospect value function and the weight function are given based on the relative kernel and prospect theory,which can determined the positive and negative ideal schemes.Next,the positive and negative incidence coefficients are given based on the grey relational analysis,and then the comprehensive close degree is determined to sort the schemes.Finally,an example is presented to illustrate the validity and rationality of the proposed method.
引文
[1]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004:1-2.
[2]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002.
[3]刘思峰,党耀国,方志耕等.灰色系统理论及其应用[M].北京:科学出版社,2010:275-278.
[4]张岐山,郭喜江,邓聚龙.灰关联熵分析方法[J].系统工程理论与实践,1996(8):8-12.
[5]蒋诗泉,刘思峰,刘中侠,方志耕.基于面积的灰色关联决策模型[J].控制与决策,2015,30(4):685-690.
[6]罗党,刘思峰.灰色关联决策方法研究[J].中国管理科学,2005(1):102-107.
[7]Kahneman D,,Tversky A.Prospect theory:Analysis of decision under risk[J].Econometric,1979,47(2):263-291.
[8]Tversky A,Kahneman D.Advances in prospect theory:Cumulative representation of uncertainty[J].Journal of Risk and Uncertainty,1992,5(3):297-323.
[9]王正新,党耀国,裴玲玲,王砚羽.基于累积前景理论的多指标灰关联决策方法[J].控制与决策,2010,25(2):232-236.
[10]龚承柱,李兰兰,卫振锋,诸克军.基于前景理论和隶属度的混合型多属性决策方法[J].中国管理科学,2014,22(10):122-128.
[11]Li Q,Zhao N.Stochastic interval-grey number VIKOR method based on prospect theory[J].Grey Systems:Theory and Application,2015,5(1):105-116.
[12]Li C B,Yuan J H,Gao P.Risk decision-making based on Mahalanobis-Taguchi system and grey cumulative prospect theory for enterprise information investment[J].Intelligent Decision Technologies,2016,10(1):49-58.
[13]罗党.三参数区间灰数信息下的决策方法[J].系统工程理论与实践,2009,29(1):124-130.
[14]王霞,党耀国.三参数区间灰数信息下的动态多属性决策方法[J].控制与决策,2015,30(9):1623-1629.
[15]闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰靶决策方法[J].控制与决策,2015,30(1):105-109.
[16]王坚强.“奖优罚劣”的动态多指标灰色关联度模型研究[J].系统工程与电子技术,2002(3):39-41.
[17]朱建军,宋传平,刘思峰,王瞄华,王梦光,一类三端点区间数判断矩阵的一致性及权重研究[J].系统工程学报,2008(1):22-27.
[2]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002.
[3]刘思峰,党耀国,方志耕等.灰色系统理论及其应用[M].北京:科学出版社,2010:275-278.
[4]张岐山,郭喜江,邓聚龙.灰关联熵分析方法[J].系统工程理论与实践,1996(8):8-12.
[5]蒋诗泉,刘思峰,刘中侠,方志耕.基于面积的灰色关联决策模型[J].控制与决策,2015,30(4):685-690.
[6]罗党,刘思峰.灰色关联决策方法研究[J].中国管理科学,2005(1):102-107.
[7]Kahneman D,,Tversky A.Prospect theory:Analysis of decision under risk[J].Econometric,1979,47(2):263-291.
[8]Tversky A,Kahneman D.Advances in prospect theory:Cumulative representation of uncertainty[J].Journal of Risk and Uncertainty,1992,5(3):297-323.
[9]王正新,党耀国,裴玲玲,王砚羽.基于累积前景理论的多指标灰关联决策方法[J].控制与决策,2010,25(2):232-236.
[10]龚承柱,李兰兰,卫振锋,诸克军.基于前景理论和隶属度的混合型多属性决策方法[J].中国管理科学,2014,22(10):122-128.
[11]Li Q,Zhao N.Stochastic interval-grey number VIKOR method based on prospect theory[J].Grey Systems:Theory and Application,2015,5(1):105-116.
[12]Li C B,Yuan J H,Gao P.Risk decision-making based on Mahalanobis-Taguchi system and grey cumulative prospect theory for enterprise information investment[J].Intelligent Decision Technologies,2016,10(1):49-58.
[13]罗党.三参数区间灰数信息下的决策方法[J].系统工程理论与实践,2009,29(1):124-130.
[14]王霞,党耀国.三参数区间灰数信息下的动态多属性决策方法[J].控制与决策,2015,30(9):1623-1629.
[15]闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰靶决策方法[J].控制与决策,2015,30(1):105-109.
[16]王坚强.“奖优罚劣”的动态多指标灰色关联度模型研究[J].系统工程与电子技术,2002(3):39-41.
[17]朱建军,宋传平,刘思峰,王瞄华,王梦光,一类三端点区间数判断矩阵的一致性及权重研究[J].系统工程学报,2008(1):22-27.