支付值为梯形直觉模糊数的改进矩阵博弈求解方法
|
摘要
针对支付值为梯形直觉模糊数的矩阵博弈求解问题,提出了一种改进的基于加权均值及模糊度排序的线性规划求解方法。引入梯形直觉模糊数均值和模糊度的概念及基于加权均值模糊度的排序方法,从而构建改进的线性规划模型,计算得到局中人的最优策略。结合市场销售博弈问题,数值实例表明了所提方法的合理性和有效性。
For the problem of matrix games with payoffs of intuitionistic trapezoidal fuzzy numbers,a modified linear programming solving method is proposed based on weighted value index and ambiguity index. Firstly,the concepts of value index and ambiguity index of trapezoidal intuitionistic fuzzy numbers are introduced,and the ranking method based on them is given. Then,a modified linear programming based on the ranking method is proposed to compute the optimal strategies.Finally,an illustrative example of market games is given to demonstrate the feasibility and validity of the developed method.
For the problem of matrix games with payoffs of intuitionistic trapezoidal fuzzy numbers,a modified linear programming solving method is proposed based on weighted value index and ambiguity index. Firstly,the concepts of value index and ambiguity index of trapezoidal intuitionistic fuzzy numbers are introduced,and the ranking method based on them is given. Then,a modified linear programming based on the ranking method is proposed to compute the optimal strategies.Finally,an illustrative example of market games is given to demonstrate the feasibility and validity of the developed method.
引文
[1]NEUMANN J V,MORGENSTERN O.The Theory of Games and Economic Behavior[M].Princeton:Princeton University Press,1944.
[2]BECTOR C R,CHANDRA S,VIJAY V.Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs[J].Fuzzy Sets and Systems,2004,146(2):253-269.
[3]BECTOR C R,CHANDRA S.Fuzzy mathematical programming and fuzzy matrix games[M].Berlin:Springer Verlag,2005.
[4]VIJAY V,MEHRA A,CHANDRA S,et al.Fuzzy matrix games via a fuzzy ralation approach[J].Fuzzy Optimization and Decision Making,2007,6(4):299-314.
[5]LI D F.An effective methodology for solving matrix games with fuzzy payoffs[J].IEEE Transactions on Cybernatics,2013,43(2):610-621.
[6]LI D F.A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers[J].European Journal of Operational Research,2012,223:421-429.
[7]CEVIKEL A C,AHLATCIOGLU M.A linear Interactive solution concept for fuzzy multiobjective games[J].European Journal of Pure and Applied Mathematics,2010,3(1):107-117.
[8]KOCKEN H G,OZKOK B A,TIRYAKI F.A compensatory fuzzy approach to multi-objective linear transportation problem with fuzzy parameters[J].European Journal of Pure and Applied Mathematics,2014,7(3):369-386.
[9]SEIKH M R,NAYAK P K,PAL M.An alternative approach for solving fuzzy matrix games[J].International Journal of Mathematics and Soft Computing,2016,5(1):79-92.
[10]ATANASSOV K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[11]南江霞,安京京,汪亭,等.支付值为直觉模糊集的矩阵对策的线性规划求解方法[J].数学的实践与认识,2015,45(24):176-182.
[12]NAN J X,ZHANG M J,LI D F.A methodology for matrix games with payoffs of triangular intuitionistic fuzzy number[J].Journal of Intelligent&Fuzzy Systems,2014,26:2899-2912.
[13]NAN J X,LI D F,ZHANG M J.A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers[J].International Journal of Computational Intelligence Systems,2010,3(3):280-289.
[14]VERMA T,KUMAR A.A note on“A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers”[J].International Journal of Computational Intelligence Systems,2016,8(4):690-700.
[15]SEIKH M R,NAYAK P K,PAL M.Solving bi-matrix games with pay-offs of triangular intuitionistic fuzzy numbers[J].European Journal of Pure and Applied Mathematics,2015,8(2):153-171.
[16]VERMA T,KUMAR A,APPADOO S S.Modified difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers[J].Journal of Intelligent&Fuzzy Systems,2015,29:1607-1618.
[17]杨洁,李登峰.求解梯形模糊矩阵对策的线性规划方法[J].控制与决策,2015,30(7):1219-1226.
[18]万树平,张小路.基于加权可能性均值的直觉梯形模糊数矩阵博弈求解方法[J].控制与决策,2012,27(8):1121-1126,1132.
[19]LI D F.A note on“Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly”[J].Microelectronics Reliability,2008,48(10):1741.
[20]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.
[21]LI D F,YANG J.A difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers[J].Journal of Applied Mathematics,2013(3):1-10.
[22]林友谅,李武,韩庆兰.直觉模糊数密度集成算子及其应用[J].控制与决策,2017,32(6):1026-1032.
[23]安京京,李登峰,南江霞.直觉模糊数加权高度排序法[J].系统科学与数学,2017,37(9):1949-1959.
[24]王蕊,于宪伟.基于新得分函数的直觉模糊多属性决策方法[J].模糊系统与数学,2016,30(4):102-106.
[2]BECTOR C R,CHANDRA S,VIJAY V.Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs[J].Fuzzy Sets and Systems,2004,146(2):253-269.
[3]BECTOR C R,CHANDRA S.Fuzzy mathematical programming and fuzzy matrix games[M].Berlin:Springer Verlag,2005.
[4]VIJAY V,MEHRA A,CHANDRA S,et al.Fuzzy matrix games via a fuzzy ralation approach[J].Fuzzy Optimization and Decision Making,2007,6(4):299-314.
[5]LI D F.An effective methodology for solving matrix games with fuzzy payoffs[J].IEEE Transactions on Cybernatics,2013,43(2):610-621.
[6]LI D F.A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers[J].European Journal of Operational Research,2012,223:421-429.
[7]CEVIKEL A C,AHLATCIOGLU M.A linear Interactive solution concept for fuzzy multiobjective games[J].European Journal of Pure and Applied Mathematics,2010,3(1):107-117.
[8]KOCKEN H G,OZKOK B A,TIRYAKI F.A compensatory fuzzy approach to multi-objective linear transportation problem with fuzzy parameters[J].European Journal of Pure and Applied Mathematics,2014,7(3):369-386.
[9]SEIKH M R,NAYAK P K,PAL M.An alternative approach for solving fuzzy matrix games[J].International Journal of Mathematics and Soft Computing,2016,5(1):79-92.
[10]ATANASSOV K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[11]南江霞,安京京,汪亭,等.支付值为直觉模糊集的矩阵对策的线性规划求解方法[J].数学的实践与认识,2015,45(24):176-182.
[12]NAN J X,ZHANG M J,LI D F.A methodology for matrix games with payoffs of triangular intuitionistic fuzzy number[J].Journal of Intelligent&Fuzzy Systems,2014,26:2899-2912.
[13]NAN J X,LI D F,ZHANG M J.A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers[J].International Journal of Computational Intelligence Systems,2010,3(3):280-289.
[14]VERMA T,KUMAR A.A note on“A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers”[J].International Journal of Computational Intelligence Systems,2016,8(4):690-700.
[15]SEIKH M R,NAYAK P K,PAL M.Solving bi-matrix games with pay-offs of triangular intuitionistic fuzzy numbers[J].European Journal of Pure and Applied Mathematics,2015,8(2):153-171.
[16]VERMA T,KUMAR A,APPADOO S S.Modified difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers[J].Journal of Intelligent&Fuzzy Systems,2015,29:1607-1618.
[17]杨洁,李登峰.求解梯形模糊矩阵对策的线性规划方法[J].控制与决策,2015,30(7):1219-1226.
[18]万树平,张小路.基于加权可能性均值的直觉梯形模糊数矩阵博弈求解方法[J].控制与决策,2012,27(8):1121-1126,1132.
[19]LI D F.A note on“Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly”[J].Microelectronics Reliability,2008,48(10):1741.
[20]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.
[21]LI D F,YANG J.A difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers[J].Journal of Applied Mathematics,2013(3):1-10.
[22]林友谅,李武,韩庆兰.直觉模糊数密度集成算子及其应用[J].控制与决策,2017,32(6):1026-1032.
[23]安京京,李登峰,南江霞.直觉模糊数加权高度排序法[J].系统科学与数学,2017,37(9):1949-1959.
[24]王蕊,于宪伟.基于新得分函数的直觉模糊多属性决策方法[J].模糊系统与数学,2016,30(4):102-106.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |