基于邻域互信息的区间DEA交叉效率评价方法
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摘要
传统的交叉效率评价方法多数是采用一个模型进行求解,并且往往会出现多个决策单元(DMU)均有效,因此不能对所有的决策单元进行充分排序。文章基于区间DEA,同时用进取型、仁慈型和竞合交叉效率模型进行求解,并对竞合模型中的分组方法进行改进,提出利用区间值邻域互信息进行分组,之后利用潜在信息函数对三个模型的效率分数进行集结,得到每个决策单元最终的效率分数及排名结果。最后通过一个算例验证了所提方法的合理性和可行性。
Most of the traditional cross-efficiency evaluation methods use one model to solve problems, and tend to show up multiple efficient decision-making units(DMU), thus it is unable to sufficiently order all decision units. Based on interval DEA,this paper uses aggressive approach, benevolent approach and competing cross efficiency models to solve problems, improves the grouping method in the competition model, and proposes using interval valued neighborhood mutual information to group. Then the paper utilizes the potential information function to assemble the efficiency scores of the three models to obtain the final efficiency score and ranking result of each DMU. Finally, an example is given to verify the rationality and feasibility of the proposed method.
Most of the traditional cross-efficiency evaluation methods use one model to solve problems, and tend to show up multiple efficient decision-making units(DMU), thus it is unable to sufficiently order all decision units. Based on interval DEA,this paper uses aggressive approach, benevolent approach and competing cross efficiency models to solve problems, improves the grouping method in the competition model, and proposes using interval valued neighborhood mutual information to group. Then the paper utilizes the potential information function to assemble the efficiency scores of the three models to obtain the final efficiency score and ranking result of each DMU. Finally, an example is given to verify the rationality and feasibility of the proposed method.
引文
[1]Charnes A,Cooper W W,Rhodes E.Measuring the Efficiency of Decision Making Units[J].European Journal Of Operational Research,1978,2(6).
[2]魏权龄.数据包络分析(DEA)[M].北京:科学出版社,2004.
[3]Sexton T R,Silkman R H,Hogan A.Data Envelopment Analysis:Critique and Extensions[M].San Francisco:Jossey,1986(32).
[4]Doyle J,Green R.Efficiency and Cross-efficiency in DEA:Derivations,Meanings and Uses[J].Journal of the Operational Research Society,1994,45(5).
[5]Jahanshahloo G R,Khodabakhshi M,Hosseinzadeh Lotfi F,et al.Corrigendum to A Cross-efficiency Model Based on Super-efficiency for Ranking Units Through TOPSIS Approach and Its Extension to Interval Case[J].Mathematical&Computer Modeling,2011,54(11).
[6]杨锋,夏琼,梁樑.同时考虑决策单元竞争与合作关系的DEA交叉效率评价方法[J].系统工程理论与实践,2011,31(1).
[7]李春好,苏航,佟轶杰等.基于理想决策单元参照求解策略的DEA交叉效率评价模型[J].中国管理科学,2015,23(2).
[8]范建平,岳未祯,吴美琴.基于误差传递和熵的区间DEA方法[J].系统工程理论与实践,2015,35(5).
[9]Bagherikahvarin M,Smet Y D.A Ranking Method Based on DEA and Promethee II(a rank based on DEA&PR.II)[J].Measurement,2016(89).
[10]王庆,刘学鹏,张阳.基于共识评价视角的加权DEA交叉效率评价方法[J].统计与决策,2017,(12).
[11]Shannon C E.The Mathematical Theory of Communication[J].The Bell System Technical Journal,1948,(27).
[12]Hu Q,Zhang L,Zhang D,et al.Measuring Relevance Between Discrete and Continuous Features Based on Neighborhood Mutual Information[J].Expert Systems With Applications an International Journal,2011,38(9).
[13]Hu Q,Pan W,An S,et al.An Efficient Gene Selection Technique for Cancer Recognition Based on Neighborhood Mutual Information[J].International Journal of Machine Learning&Cybernetics,2010,1.
[14]Legg P A,Rosin P L,Marshall D,et al.Feature Neighbourhood Mutual Information for Multi-modal Image Registration[J].Pattern Recognition,2015,48(6).
[15]Sadiq R,Tesfamariam S.Probability Density Functions Based Weights for Ordered Weighted Averaging(OWA)Operators:An Example of Water Quality Indices[J].European Journal of Operational Research,2007,182(3).
[16]Chang C J,Li D C,Dai W L,et al.A Latent Information Function to Extend Domain Attributes to Improve the Accuracy of Small-data-set Forecasting[J].Neurocomputing,2014,129(5).
[17]Wu L,Liu S,Yang Y.A Model to Determine OWA Weights and Its Application in Energy Technology Evaluation[J].International Journal of Intelligent Systems,2015,30(7).
[18]Despotis D K,Smirlis Y G.Data Envelopment Analysis With Imprecise Data[J].European Journal of Operational Research,2002,(140).
[19]Cooper W W,Park K S,Yu G.Idea and Ar-Idea:Models for Dealing With Imprecise Data in Dea[J].Management Science,1999,45(4).
[2]魏权龄.数据包络分析(DEA)[M].北京:科学出版社,2004.
[3]Sexton T R,Silkman R H,Hogan A.Data Envelopment Analysis:Critique and Extensions[M].San Francisco:Jossey,1986(32).
[4]Doyle J,Green R.Efficiency and Cross-efficiency in DEA:Derivations,Meanings and Uses[J].Journal of the Operational Research Society,1994,45(5).
[5]Jahanshahloo G R,Khodabakhshi M,Hosseinzadeh Lotfi F,et al.Corrigendum to A Cross-efficiency Model Based on Super-efficiency for Ranking Units Through TOPSIS Approach and Its Extension to Interval Case[J].Mathematical&Computer Modeling,2011,54(11).
[6]杨锋,夏琼,梁樑.同时考虑决策单元竞争与合作关系的DEA交叉效率评价方法[J].系统工程理论与实践,2011,31(1).
[7]李春好,苏航,佟轶杰等.基于理想决策单元参照求解策略的DEA交叉效率评价模型[J].中国管理科学,2015,23(2).
[8]范建平,岳未祯,吴美琴.基于误差传递和熵的区间DEA方法[J].系统工程理论与实践,2015,35(5).
[9]Bagherikahvarin M,Smet Y D.A Ranking Method Based on DEA and Promethee II(a rank based on DEA&PR.II)[J].Measurement,2016(89).
[10]王庆,刘学鹏,张阳.基于共识评价视角的加权DEA交叉效率评价方法[J].统计与决策,2017,(12).
[11]Shannon C E.The Mathematical Theory of Communication[J].The Bell System Technical Journal,1948,(27).
[12]Hu Q,Zhang L,Zhang D,et al.Measuring Relevance Between Discrete and Continuous Features Based on Neighborhood Mutual Information[J].Expert Systems With Applications an International Journal,2011,38(9).
[13]Hu Q,Pan W,An S,et al.An Efficient Gene Selection Technique for Cancer Recognition Based on Neighborhood Mutual Information[J].International Journal of Machine Learning&Cybernetics,2010,1.
[14]Legg P A,Rosin P L,Marshall D,et al.Feature Neighbourhood Mutual Information for Multi-modal Image Registration[J].Pattern Recognition,2015,48(6).
[15]Sadiq R,Tesfamariam S.Probability Density Functions Based Weights for Ordered Weighted Averaging(OWA)Operators:An Example of Water Quality Indices[J].European Journal of Operational Research,2007,182(3).
[16]Chang C J,Li D C,Dai W L,et al.A Latent Information Function to Extend Domain Attributes to Improve the Accuracy of Small-data-set Forecasting[J].Neurocomputing,2014,129(5).
[17]Wu L,Liu S,Yang Y.A Model to Determine OWA Weights and Its Application in Energy Technology Evaluation[J].International Journal of Intelligent Systems,2015,30(7).
[18]Despotis D K,Smirlis Y G.Data Envelopment Analysis With Imprecise Data[J].European Journal of Operational Research,2002,(140).
[19]Cooper W W,Park K S,Yu G.Idea and Ar-Idea:Models for Dealing With Imprecise Data in Dea[J].Management Science,1999,45(4).