基于Zhenyuan积分的直觉模糊多属性决策方法
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摘要
针对属性之间具有相互关联关系的直觉模糊多属性决策问题,提出一种基于Zhenyuan积分的决策方法.首先提出直觉模糊Zhenyuan积分平均(IFZA)算子;然后探讨IFZA算子的优良性质以及与现有直觉模糊集成算子的关系,研究表明,IFZA算子可以改进现有直觉模糊奇异积分算子的缺陷,能够全面度量属性之间的相互关联关系;最后提出一种基于IFZA算子的属性间具有相互关联关系的直觉模糊多属性决策方法,并通过实例验证所提出方法的有效性和可行性.
With regard to intuitionistic fuzzy multiple attribute decision making with interaction between attributes, a method based on the Zhenyuan integral is presented. The intuitionistic fuzzy Zhenyuan averaging(IFZA) operator is developed, and some of its desirable properties are studied. The research shows that the IFZA operator can fully consider the importance of interactions among different attributes and improve the intuitionistic fuzzy Choquet integral operator.Finally, a method based on the IFZA for intuitionistic fuzzy multiple attribute decision making is introduced, and a numerical example is provided to illustrate the effectiveness and applicability of the presented method.
With regard to intuitionistic fuzzy multiple attribute decision making with interaction between attributes, a method based on the Zhenyuan integral is presented. The intuitionistic fuzzy Zhenyuan averaging(IFZA) operator is developed, and some of its desirable properties are studied. The research shows that the IFZA operator can fully consider the importance of interactions among different attributes and improve the intuitionistic fuzzy Choquet integral operator.Finally, a method based on the IFZA for intuitionistic fuzzy multiple attribute decision making is introduced, and a numerical example is provided to illustrate the effectiveness and applicability of the presented method.
引文
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[3]徐泽水.直觉模糊信息集成理论及应用[M].北京:科学出版社,2008:10-62.(Xu Z S.Intuitionistic fuzzy information aggregation:Theory and applications[M].Beijing:Science Press,2008:10-62.)
[4]Atanassov K T.Intuitionistic fuzzy sets:Theory and applications[M].Heidelberg:Physica-Verlag,1999:25-50.
[5]李登峰.直觉模糊集决策与对策分析方法[M].北京:国防工业出版社,2012:8-36.(Li D F.Intuitionistic fuzzy set decision making and game analysis methodologies[M].Beijing:National Defense Industry Press,2012:8-36.)
[6]Xu Z S.Intuitionistic fuzzy aggregation operators[J].IEEE Trans on Fuzzy Systems,2007,15(6):1179-1187.
[7]余高锋,李登峰,邱锦明.一类直觉模糊线性规划的求解及其应用[J].控制与决策,2015,30(4):640-644.(Yu G F,Li D F,Qiu J M.Solution to intuitionistic fuzzy linear programming and its application[J].Control and Decision,2015,30(4):640-644.)
[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]曾守桢.基于直觉模糊信息的综合评价问题研究[D].杭州:浙江工商大学统计与数学学院,2013.(Zeng S Z.Study on the comprehensive evaluation technology based on intuitionistic fuzzy information[D].Hangzhou:School of Statistics and Mathematics,Zhejiang Gongshang University,2013.)
[10]陈岩,李庭.基于Choquet积分的直觉不确定语言信息集结算子及其应用[J].控制与决策,2016,31(5):842-852.(Chen Y,Li T.Intuitionistic uncertain linguistic information aggregation operatorsbased on Choquet integral and their application[J].Control and Decision,2016,31(5):842-852.)
[11]Grabisch M.The application of fuzzy integrals in multi-criteria decision making[J].European J of Operational Research,1996,89(3):445-456.
[12]Tan C Q.A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS[J].Expert Systems with Applications,2011,38(4):3023-3033.
[13]Tan C Q,Chen X H.Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making[J].Expert Systems with Applications,2010,37(1):149-157.
[14]Xu Z S.Choquet integrals of weighted intuitionistic fuzzy information[J].Information Sciences,2010,180(5):726-736.
[15]Wu J Z,Chen F,Nie C P,et al.Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making[J].Information Sciences,2013,222(4):509-527.
[16]Wang Z Y,Leung K S,Wong M L,et al.A new type of nonlinear integrals and the computational algorithm[J].Fuzzy Sets and Systems,2000,112(2):223-231.
[17]Chen S M,Tan J M.Handling multicriteria fuzzy decision making problems based on vague set theory[J].Fuzzy Sets and Systems,1994,67(2):163-172.
[18]Hong D H,Choi C H.Multicriteria fuzzy decision making problems based on vague set theory[J].Fuzzy Sets and Systems,2000,114(1):103-113.
[19]Wang Z Y,Klir G J.Fuzzy measure theory[M].New York:Plenum Press,1992:30-75.
[20]王熙照.模糊测度和模糊积分及在分类技术中的应用[M].北京:科学出版社,2008:21-72.(Wang X Z.Fuzzy measures and fuzzy integral and their application in classification technique[M].Beijing:Science Press,2008:21-72.)