具有风险偏好的模糊网络最短路算法  

Arithmetic of Shortest Path About Fuzzy Network Which Possessed Risk-preference

作　　者：闫艳[1] 岳立柱[1] 仲维清[1] 

机构地区：[1]辽宁工程技术大学工商管理学院,辽宁阜新123000

出　　处：《数学的实践与认识》2010年第13期110-116,共7页Mathematics in Practice and Theory

基　　金：辽宁省教育厅高效创新团队项目计划(2006T076;2006T077)

摘　　要：运用结构元理论来求解具有风险偏好的、带有模糊权值的网络最短路问题.首先,简要介绍模糊结构元及相关定理.之后,提出了组合序,证明组合序是全序.组合序含有参数θ,随着θ的取值范围不同,序反映风险偏好的类型不同.在组合序和相关定理的基础上,证明了模糊网络最短路的判定定理,定理表明:求模糊网络最短路等价求一经典网络最短路,且风险偏好大小由θ的取值来确定.最后,通过一个例子来说明求解过程.Using the theory of structured element to solve the shortest path network which possesses risk- preference, fuzzy weight value . First I introduced briefly fuzzy structured element and the related theorey. Then , After combined-order is presented and it is proved that is complete order, there is parameterθ in combined-order, with the different θ, the order reflects the different types of risk , based on the combined-order and the related theorem,it is proved how to justify the theorey of the fuzzy network shortest path,and it is showed that solving shortest path of fuzzy network is equivalent to solving a classical shortest-circuit network, risk- preferences is decided by θ.Finally, an example to illustrate the process of solving.

关 键 词：模糊数 网络图 最小费用 结构元 

分 类 号：O224[理学—运筹学与控制论]