一类赋权图的优化  

Optimization of a Kind of Weighted Graphs

作　　者：严喜祖[1] 宋中民[1] 

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2010年第3期165-168,共4页Journal of Yantai University(Natural Science and Engineering Edition)

摘　　要：为了扩展赋权图的应用领域,灰色赋权图被定义,并根据灰色系统的理论和方法研究了这类赋权图的优化问题.灰色赋权图是在不确定情况下制定决策的一种灰色模型,它是传统赋权图模型的一种发展.在灰色赋权图模型中,灰数被引进表达不确定信息,这些灰信息进入优化过程会产生不确定的结果.针对目标函数中具有灰系数的不确定优化问题,从主客观因素出发,提出了确定满意子图的多目标解决方法,实例分析表明这种把主客观因素结合的方法,比较合理.The grey weighted graph is introduced for expanding application field of the weighted graph and the optimization problems of the grey weighted graph are discussed according to grey systems theory and methods.The grey weighted graph is a grey model for decision making under uncertainty and is a development of traditional weighted graph model.In a grey weighted graph model,grey numbers are introduced to express uncertain messages.Grey messages are communicated into the optimization processes and generate uncertainty in the results.For the uncertainty optimization problems with grey number coefficients in objective functions,from subjective and objective factors,the method of the multiobjective looking for satisfactory subgraph is advanced and an example is provided to verify the feasibility of this method which combines subjective factors with objective ones.

关 键 词：最优化 不确定性 灰数 赋权图 

分 类 号：O157.5[理学—数学]