群体多目标决策联合超有效解的广义梯度型最优性条件  

Optimality Conditions for Joint Superly Efficient Solutions of Group Multiobjective Decision Making in the Sense of Generalized Gradient

作　　者：徐义红[1] 肖明丽[1] 涂相求[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2013年第2期176-179,共4页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(61175127);江西省自然科学基金资助项目(20122BAB201003);江西省教育厅科技资助项目(GJJ12010)

摘　　要：在Hausdorff局部凸拓扑线性空间中,借助切锥引进了超有效广义梯度概念。对于群体多目标决策问题,利用供选方案的超有效数,引进了集值映射的联合超有效解。利用切锥的性质建立了联合超有效解在广义梯度意义下的最优性必要条件,利用超有效解集的性质得到了充分条件。推广了现有文献的相关结论。In Hausdorff locally convex spaces,superly efficient generalized gradient was introduced with the help of contingent cone.For group multiobjective decision making problems,the joint superly efficient solutions of set-valued maps were introduced by means of superly efficient numbers of alternatives.The optimality necessary condition for the joint superly efficient solutions was established in the sense of generalized gradient by using of properties for contingent cone.Optimality sufficient condition was obtained using the properties for the set of superly efficient solutions.Some relevant conclusions were extended in recent references.

关 键 词：群体决策 多目标决策 联合超有效解 超有效广义梯度 最优性条件 

分 类 号：O224[理学—运筹学与控制论]