一类系数为梯形模糊数的两层多随从线性规划模型
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摘要
针对一类系数为梯形模糊数的两层多随从线性规划问题,利用模糊结构元理论定义了模糊结构元加权序,证明了一类系数为梯形模糊数的两层多随从线性规划问题的最优解等价于两层多随从线性规划问题的最优解.根据线性规划的对偶定理和互补松弛性质,得到了两层多随从线性规划模型的最优化条件.最后,利用两层多随从线性规划模型的最优化条件,设计了求解一类系数为梯形模糊数的两层多随从线性规划问题的算法,并通过算例验证了该方法的可行性和合理性.
Aimin g at a class of coefficients for trapezoidal fuzzy numbers of linear bilevel programming problem with multiple followers,using fuzzy structured element theory to define the fuzzy structured element weighted order,which proving a class of coefficients for trapezoidal fuzzy numbers of linear bilevel programming problem of the optimal solution with multiple followers is equivalent to a linear bilevel programming problem of the optimal solution with multiple followers(MFBLP).According to the duality theory of linear programming and the properties of complementary relaxation,obtaining the optimal conditions of MFBLP.Finally,designing algorithm for solving a class of trapezoidal fuzzy numbers for linear bilevel programming problem with multiple followers by using the optimal conditions of MFBLP,and numerical examples demonstrating the feasibility and rationality of the method.
Aimin g at a class of coefficients for trapezoidal fuzzy numbers of linear bilevel programming problem with multiple followers,using fuzzy structured element theory to define the fuzzy structured element weighted order,which proving a class of coefficients for trapezoidal fuzzy numbers of linear bilevel programming problem of the optimal solution with multiple followers is equivalent to a linear bilevel programming problem of the optimal solution with multiple followers(MFBLP).According to the duality theory of linear programming and the properties of complementary relaxation,obtaining the optimal conditions of MFBLP.Finally,designing algorithm for solving a class of trapezoidal fuzzy numbers for linear bilevel programming problem with multiple followers by using the optimal conditions of MFBLP,and numerical examples demonstrating the feasibility and rationality of the method.
引文
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[14]刘海涛,郭嗣琮.基于结构元方法的可能性规划[J].数学的实践与认识,2012,42(8):106-111
[15]周喜华,石盟盟,邓胜岳,彭金花.一类系数为梯形模糊数的整数规划[J].数学的实践与认识,2017,47(3):171178.
[2]Dantzig G B,Wolfe P.The Decomposition Principle For Linear programming[J].Operations Research,1960,8:101-111.
[3]Candler W and Norton R D.Multilevel programming and development policy[R].World Bank staff Working Paper,1977,258,Washington D C.
[4]Migdals.Bilevel program ming in traffic planning.Models,method sand challenge[J].Journal of Global Optimization,1995,7:381-405
[5]张小宁·双层优化交通模型及其算法[J].同济大学学报(自然科学版),2005,32(2):69-73.
[6]肖剑,但斌,张旭梅.供货商选择的双层规划模型及遗传算法求解[J].重庆大学学报(自然科学版),2007,30(6):156-158.
[7]赵志刚,顾新一.求解供应链分销模型的双层规划方法[J].上海理工大学报,2006,28(3):300-301.
[8]Gailly B,Boulier F,Installe M.Application of multicriteria and multiperson decision making to the planning of the developing of rural areas,support systems for decision and negotiation process[M].Warsaw:Polish Academic Press,1992.141-146.
[9]付永红,杜纲·具有模糊系数的两层线性规划[J].管理科学学报,1999,2(1):42-49.
[10]赵海坤,郭嗣琮.全系数模糊两层线性规划[J].模糊系数与数学,2010,6:98-108.
[11]郭嗣琮.基于模糊结构元理论的模糊分析数学原理[M].沈阳:东北大学,2004:54-62
[12]周喜华,黄晓红,陈敏娜,邓胜岳,周婷.一类系数为梯形模糊数的两层线性规划[J].数学的实践与认识,2017,47(4):206-214.
[13]郭嗣琮.模糊实数空间与[-1,1]上同序单调函数类的同胚[J].自然科学进展,2004,11:1318-1321.
[14]刘海涛,郭嗣琮.基于结构元方法的可能性规划[J].数学的实践与认识,2012,42(8):106-111
[15]周喜华,石盟盟,邓胜岳,彭金花.一类系数为梯形模糊数的整数规划[J].数学的实践与认识,2017,47(3):171178.