基于熵权Vague集的多目标决策方法
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摘要
针对目前基于Vague集的多目标决策中目标权重的主观任意性以及评价函数的单一性问题,提出一种基于熵权Vague集的多目标决策方法。首先,将决策矩阵转化为目标优属度矩阵,再利用熵权系数法计算各个目标的客观权重,综合考虑客观权重和主观权重得到各个目标的权重向量区间;然后,通过计算方案的支持目标集、反对目标集和中立目标集得出方案的Vague估计值;最后,定义新的评价函数对方案进行排序并选出最优方案。通过算例验证了所提方法的合理性和有效性。
In view of the subjective arbitrariness of objective weight in multi-objective decision making based on Vague sets and the monotong problem of evaluation function, a novel approach to multi-objective decision making based on entropy weighted-Vague sets was presented. Firstly, the decision matrix was transformed into the objective-grade-membership matrix.Then the objective weight of each objective was calculated by entropy coefficient method, and the weight vector interval of each objective was obtained by considering objective weight and subjective weight. Next the Vague evaluation was obtained by computing the sets of objectives being in favor, against and neutral. Finally, a new evaluation function was defined to sort the alternatives and select the optimal scheme. The rationality and effectiveness of the method were verified by an example.
In view of the subjective arbitrariness of objective weight in multi-objective decision making based on Vague sets and the monotong problem of evaluation function, a novel approach to multi-objective decision making based on entropy weighted-Vague sets was presented. Firstly, the decision matrix was transformed into the objective-grade-membership matrix.Then the objective weight of each objective was calculated by entropy coefficient method, and the weight vector interval of each objective was obtained by considering objective weight and subjective weight. Next the Vague evaluation was obtained by computing the sets of objectives being in favor, against and neutral. Finally, a new evaluation function was defined to sort the alternatives and select the optimal scheme. The rationality and effectiveness of the method were verified by an example.
引文
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[2]LIANG T F.Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain[J].Computers&Industrial Engineering,2008,55(3):676-694.
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[4]周艳,贾建斌.模糊多目标群决策方法在军事辅助中的运用[J].数学的实践与认识,2009,29(13):38-42.(ZHOU Y,JIA J B.Application of fuzzy multi-objective group decision method in military assistance[J].Mathematics in Practice and Theory,2009,29(13):38-42.)
[5]SMITH E B.The motion control of a mobile robot using multi-objective decision making[C]//Proceedings of the 47th Annual Southeast Regional Conference.New York:ACM,2009:1-6.
[6]GAU W L,BUEHRER D J.Vague sets[J].IEEE Transactions on System,Man,and Cybernetics,1993,23(2):403-614.
[7]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.
[8]HONG D H,CHOI C H.Handling multi-criteria fuzzy decisionmaking problems based on Vague sets theory[J].Fuzzy Sets and Systems,2000,114(1):103-113.
[9]李凡,卢安,蔡立晶.基于Vague集的多目标模糊决策方法[J].华中科技大学学报:自然科学版,2001,29(7):1-3.(LI F,LUA,CAI L J.Multicriteria decision making based on Vague set[J].Journal of Huazhong University of Science and Technology of Science and Technolgoy,2001,29(7):1-3.)
[10]刘华文.多目标模糊决策的Vague集方法[J].系统理论工程与实践,2004,24(5):103-109.(LIU H W.Vague set methods of multicriteria fuzzy decision making[J].Systems Engineering-Theory&Practice,2004,24(5):103-109.)
[11]周珍,吴祈宗.基于Vague集的多准则模糊决策方法[J].小型微型计算机系统,2005,26(8):1350-1353.(ZHOU Z,WU Q Z.Multicriteria fuzzy decision making method based on Vague set[J].Journal of Chinese Computer Systems,2005,26(8):1350-1353.)
[12]王会英,张朝坤,董东.基于区间直觉模糊集的模糊多目标群决策[J].计算机应用,2013,33(4):967-970.(WANG H Y,ZHANG C K,DONG D.Fuzzy multi-objective group decision making based on interval-valued intuitionistic fuzzy set[J].Journal of Computer Application,2013,33(4):967-970.)
[13]王珏,刘三阳,张杰.基于Vague集的模糊多目标决策方法[J].系统工程理论与实践,2005,25(2):119-122.(WANG J,LIU SY,ZHANG J.Fuzzy multiple objectives decision making based on Vague sets[J].Systems Engineering-Theory&Practice,2005,25(2):119-122.)
[14]戴厚平.基于信息熵的区间直觉模糊多属性决策方法[J].重庆文理学院学报(自然科学版),2009,28(6):1-4.(DAI H P.Method for interval-valued intuitionistic fuzzy multi-attribute decision making based on information entropy[J].Journal of Chongqing University of Arts and Science(Natural Science Edition),2009,28(6):1-4.)
[15]黄松,黄卫来.基于熵权系数与Vague集的多目标决策方法[J].管理学报,2005,2(S2):120-123.(HUANG S,HUANG WL.Approach to objectives decision making based on entropy coefficient and Vague set[J].Chinese Journal of Management,2005,2(S2):120-123.)
[16]唐志刚,梁家荣,李士勇.一种基于Vague集的模糊多目标决策新方法[J].计算机技术与自动化,2006,25(4):31-34.(TANGZ G,LIANG J R,LI S Y.New fuzzy multiple objectives decision making based on Vague sets[J].Computing Technology and Automation,2006,25(4):31-34.)
[17]李登峰.模糊多目标多人决策与对策[M].北京:国防工业出版社,2002:84-93.(LI D F.Fuzzy Multiobjective Many-Person Decision Making and Games[M].Beijing:National Defense Industry Press,2002:84-93.)
[2]LIANG T F.Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain[J].Computers&Industrial Engineering,2008,55(3):676-694.
[3]吴开信.多目标模糊优选决策模型及其在资源分配中的应用[D].成都:西南交通大学,2007:49-53.(WU K X.The model of fuzzy optimal selection among multi-objectives and its application of the resources[D].Chengdu:Southwest Jiaotong University,2007:49-53.)
[4]周艳,贾建斌.模糊多目标群决策方法在军事辅助中的运用[J].数学的实践与认识,2009,29(13):38-42.(ZHOU Y,JIA J B.Application of fuzzy multi-objective group decision method in military assistance[J].Mathematics in Practice and Theory,2009,29(13):38-42.)
[5]SMITH E B.The motion control of a mobile robot using multi-objective decision making[C]//Proceedings of the 47th Annual Southeast Regional Conference.New York:ACM,2009:1-6.
[6]GAU W L,BUEHRER D J.Vague sets[J].IEEE Transactions on System,Man,and Cybernetics,1993,23(2):403-614.
[7]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.
[8]HONG D H,CHOI C H.Handling multi-criteria fuzzy decisionmaking problems based on Vague sets theory[J].Fuzzy Sets and Systems,2000,114(1):103-113.
[9]李凡,卢安,蔡立晶.基于Vague集的多目标模糊决策方法[J].华中科技大学学报:自然科学版,2001,29(7):1-3.(LI F,LUA,CAI L J.Multicriteria decision making based on Vague set[J].Journal of Huazhong University of Science and Technology of Science and Technolgoy,2001,29(7):1-3.)
[10]刘华文.多目标模糊决策的Vague集方法[J].系统理论工程与实践,2004,24(5):103-109.(LIU H W.Vague set methods of multicriteria fuzzy decision making[J].Systems Engineering-Theory&Practice,2004,24(5):103-109.)
[11]周珍,吴祈宗.基于Vague集的多准则模糊决策方法[J].小型微型计算机系统,2005,26(8):1350-1353.(ZHOU Z,WU Q Z.Multicriteria fuzzy decision making method based on Vague set[J].Journal of Chinese Computer Systems,2005,26(8):1350-1353.)
[12]王会英,张朝坤,董东.基于区间直觉模糊集的模糊多目标群决策[J].计算机应用,2013,33(4):967-970.(WANG H Y,ZHANG C K,DONG D.Fuzzy multi-objective group decision making based on interval-valued intuitionistic fuzzy set[J].Journal of Computer Application,2013,33(4):967-970.)
[13]王珏,刘三阳,张杰.基于Vague集的模糊多目标决策方法[J].系统工程理论与实践,2005,25(2):119-122.(WANG J,LIU SY,ZHANG J.Fuzzy multiple objectives decision making based on Vague sets[J].Systems Engineering-Theory&Practice,2005,25(2):119-122.)
[14]戴厚平.基于信息熵的区间直觉模糊多属性决策方法[J].重庆文理学院学报(自然科学版),2009,28(6):1-4.(DAI H P.Method for interval-valued intuitionistic fuzzy multi-attribute decision making based on information entropy[J].Journal of Chongqing University of Arts and Science(Natural Science Edition),2009,28(6):1-4.)
[15]黄松,黄卫来.基于熵权系数与Vague集的多目标决策方法[J].管理学报,2005,2(S2):120-123.(HUANG S,HUANG WL.Approach to objectives decision making based on entropy coefficient and Vague set[J].Chinese Journal of Management,2005,2(S2):120-123.)
[16]唐志刚,梁家荣,李士勇.一种基于Vague集的模糊多目标决策新方法[J].计算机技术与自动化,2006,25(4):31-34.(TANGZ G,LIANG J R,LI S Y.New fuzzy multiple objectives decision making based on Vague sets[J].Computing Technology and Automation,2006,25(4):31-34.)
[17]李登峰.模糊多目标多人决策与对策[M].北京:国防工业出版社,2002:84-93.(LI D F.Fuzzy Multiobjective Many-Person Decision Making and Games[M].Beijing:National Defense Industry Press,2002:84-93.)