基于前景理论的模拟植物生长算法研究
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摘要
针对属性值和属性权重均为区间数,决策者权重未知的多属性群决策问题,文章提出了一种基于前景理论的群体最优集结算法。文章首先以决策者可承受的心理临界值为参考点,将属性权重转化为决策者的主观概率权重,计算各决策者的方案综合前景值向量,以各决策者对方案前景值的贡献度确定决策者权重;然后,将各决策者的方案综合前景值映射到平面直角坐标系中,利用最小欧式距离的思想,采用模拟植物生长算法求解群体最优集结信息,进而根据各方案集结前景值的可能度比较实现方案的排序;最后,通过实例验证分析说明了该方法的可行性和有效性。
To solve the multi-attribute group decision-making problem with unknown attribute values and attribute probability,an optimal aggregation algorithm based on prospect theory is proposed.The psychological critical values that decision makers bear can be regarded as reference points and the interval attribute weights can be converted to subjective weights.Then,the comprehensive prospect value vectors of each decision maker are calculated.The prospect value contributions of decision makers are calculated to determine the weights of decision makers.On this basis,the prospect values are mapped to plane coordinate.By applying the plant growth simulation algorithm and using the minimum Euclidean distance,the optimal aggregation information is solved.Then,by comparing the comprehensive prospect value,alternatives are ranked.Finally,by validate experiment analysis,the feasibility and effectiveness of the proposed method is illustrated.
To solve the multi-attribute group decision-making problem with unknown attribute values and attribute probability,an optimal aggregation algorithm based on prospect theory is proposed.The psychological critical values that decision makers bear can be regarded as reference points and the interval attribute weights can be converted to subjective weights.Then,the comprehensive prospect value vectors of each decision maker are calculated.The prospect value contributions of decision makers are calculated to determine the weights of decision makers.On this basis,the prospect values are mapped to plane coordinate.By applying the plant growth simulation algorithm and using the minimum Euclidean distance,the optimal aggregation information is solved.Then,by comparing the comprehensive prospect value,alternatives are ranked.Finally,by validate experiment analysis,the feasibility and effectiveness of the proposed method is illustrated.
引文
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[2]陈振颂,李廷来.基于ITFN信息关联输入的改进群体MULTIMOORA决策方法[J].系统工程理论与实践,2014,34(12):3138-3156.
[3]WU T,LIU X W.An interval type-2fuzzy clustering solution for large-scale multiple-criteria group decisionmaking problems[J].Knowledge-Based Systems,2016(114):118-127.
[4]BAYRAM H,SAHIN R.A simulation based multi-attribute group decision making technique with decision constraints[J].Applied Soft Computing,2016(49):629-640.
[5]JOSHI D,KUMAR S.Interval-valued intuitionistic hesitant fuzzy Choquet integral based on TOPSIS method for multi-criteria group decision making[J].European Journal of Operational Research,2016,248(1):183-191.
[6]RAMOS G M,DAAMEN W,HOOGENDOORN S.A state-of-the-art review:developments in utility theory,prospect theory and regret theory to investigate travellers'behaviour in situations involving travel time uncertainty[J].Transport Reviews.2014,34(1):46-67.
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[9]TVERSKY A,KAHNEMAN D.Advances in prospecttheory-cumulative representation of uncertainty[J].Journal of Risk and Uncertainty,1992,5(4):297-323.
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[13]QIN J D,LIU X W,PEDRYCZ W.An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2fuzzy environment[J].Knowledge-Based Systems,2015,86(C):116-130.
[14]PENG X D,YANG Y.Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight[J].Applied Soft Computing,2017(54):415-430.
[15]FAN Z P,ZHANG X,CHEN F D,et al.Multiple attribute decision making considering aspiration-levels:Amethod based on prospect theory[J].Computers&Industrial Engineering,2013,65(2):341-350.
[16]闫书丽,刘思峰.基于前景理论的群体灰靶决策方法[J].控制与决策,2014,29(4):673-678.
[17]杜元伟,段万春,缪彬.基于前景理论的交互式群组风险决策方法[J].控制与决策,2013,28(8):1183-1189.
[18]XU Z S.Dependent uncertain ordered weighted aggregation operators[J].Information Fusion,2008,9(2):310-316.
[19]XU Z S,DA Q L.The uncertain OWA operator[J].International Journal of Intelligent Systems,2002,17(6):569-575.
[20]YAGER R R.On ordered weighted averaging aggregation operators in multi-criteria decision making[J].IEEE Transactions on Systems Management&Cybernetics,1988,18(6):183-190.
[21]LIU W,LI L.An approach to determining the integrated weights of decision makers based on interval number group decision matrices[J].Knowledge-Based Systems,2015,90(C):92-98.
[22]李彤,王春峰,王文波,等.求解整数规划的一种仿生类全局优化算法-模拟植物生长算法[J].系统工程理论与实践,2005,25(1):76-85.
[23]李彤.模拟植物生长算法原理及应用[M].北京:科学出版社,2016.
[24]王淳,程浩忠.基于模拟植物生长算法的配电网重构[J].中国电机工程学报,2007,27(19):50-55.
[25]BEYNON M J.A method of aggregation in DS/AHPfor group decision-making with the non-equivalent importance of individuals in the group[J].Computers and Operations Research,2005,32(7):1881-1896.
[26]王淳,程浩忠.模拟植物生长算法及其在输电网规划中的应用[J].电子系统自动化,2007,31(7):24-28.
[2]陈振颂,李廷来.基于ITFN信息关联输入的改进群体MULTIMOORA决策方法[J].系统工程理论与实践,2014,34(12):3138-3156.
[3]WU T,LIU X W.An interval type-2fuzzy clustering solution for large-scale multiple-criteria group decisionmaking problems[J].Knowledge-Based Systems,2016(114):118-127.
[4]BAYRAM H,SAHIN R.A simulation based multi-attribute group decision making technique with decision constraints[J].Applied Soft Computing,2016(49):629-640.
[5]JOSHI D,KUMAR S.Interval-valued intuitionistic hesitant fuzzy Choquet integral based on TOPSIS method for multi-criteria group decision making[J].European Journal of Operational Research,2016,248(1):183-191.
[6]RAMOS G M,DAAMEN W,HOOGENDOORN S.A state-of-the-art review:developments in utility theory,prospect theory and regret theory to investigate travellers'behaviour in situations involving travel time uncertainty[J].Transport Reviews.2014,34(1):46-67.
[7]SIMON H A.Effects of increased productivity upon the ratio of urban to rural population[J].Econometrica,1947,15(1):31-42.
[8]KAHNEMAN D,TVERSKY A.Prospect theory:an analysis of decision under risk[J].Econometrica,1979,47(2):263-292.
[9]TVERSKY A,KAHNEMAN D.Advances in prospecttheory-cumulative representation of uncertainty[J].Journal of Risk and Uncertainty,1992,5(4):297-323.
[10]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,2014,34(12):3175-3181.
[11]李鹏,吴君民,朱建军.基于新直觉模糊距离的随机决策方法[J].系统工程理论与实践,2014,34(6):1517-1524.
[12]LIU Y,FAN Z P,ZHANG Y.Risk decision analysis in emergency response:a method based on cumulative prospect theory[J].Computers&Operations Research,2014,42(2):75-82.
[13]QIN J D,LIU X W,PEDRYCZ W.An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2fuzzy environment[J].Knowledge-Based Systems,2015,86(C):116-130.
[14]PENG X D,YANG Y.Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight[J].Applied Soft Computing,2017(54):415-430.
[15]FAN Z P,ZHANG X,CHEN F D,et al.Multiple attribute decision making considering aspiration-levels:Amethod based on prospect theory[J].Computers&Industrial Engineering,2013,65(2):341-350.
[16]闫书丽,刘思峰.基于前景理论的群体灰靶决策方法[J].控制与决策,2014,29(4):673-678.
[17]杜元伟,段万春,缪彬.基于前景理论的交互式群组风险决策方法[J].控制与决策,2013,28(8):1183-1189.
[18]XU Z S.Dependent uncertain ordered weighted aggregation operators[J].Information Fusion,2008,9(2):310-316.
[19]XU Z S,DA Q L.The uncertain OWA operator[J].International Journal of Intelligent Systems,2002,17(6):569-575.
[20]YAGER R R.On ordered weighted averaging aggregation operators in multi-criteria decision making[J].IEEE Transactions on Systems Management&Cybernetics,1988,18(6):183-190.
[21]LIU W,LI L.An approach to determining the integrated weights of decision makers based on interval number group decision matrices[J].Knowledge-Based Systems,2015,90(C):92-98.
[22]李彤,王春峰,王文波,等.求解整数规划的一种仿生类全局优化算法-模拟植物生长算法[J].系统工程理论与实践,2005,25(1):76-85.
[23]李彤.模拟植物生长算法原理及应用[M].北京:科学出版社,2016.
[24]王淳,程浩忠.基于模拟植物生长算法的配电网重构[J].中国电机工程学报,2007,27(19):50-55.
[25]BEYNON M J.A method of aggregation in DS/AHPfor group decision-making with the non-equivalent importance of individuals in the group[J].Computers and Operations Research,2005,32(7):1881-1896.
[26]王淳,程浩忠.模拟植物生长算法及其在输电网规划中的应用[J].电子系统自动化,2007,31(7):24-28.