流体管网中模糊最小树的算法与分析

Algorithm and Analysis of Fuzzy Minimal Spanning Tree in Fluid Pipeline Networks

目的将模糊集应用到管网分析中,研究流体管网中模糊最小树的算法.方法利用全水平截集排序指标(OERI)法对模糊管网中的分支进行排序,在保持网络结构不变的情况下,将网络图论的常规算法适当调整,求得管网的模糊最小树.结果结合算例,既算出了树的模糊阻抗值,又针对无差异、乐观与悲观3种权重情况获得了树的OERI值,实现了模糊最小树算法.结论在保持网络结构不变的情况下,将网络图论的常规算法适当调整,既可求得管网的模糊最小树,又获得了对应不同主观权重函数时树的OERI值.

In this article, with the aid of a ranking method of fuzzy numbers, algorithms of fuzzy minimal spanning tree are obtained by applying fuzzy set to analysis of pipeline networks. By introducing the overall existence ranking index （OERI） to fuzzy numbers, order or ranking is established in the fuzzy networks. By using this fuzzy ranking method, under the condition of the original structure of the fluid network, conventional algorithms of minimal spanning tree in graph theory can be applied with appropriate modification. A numerical example is given to illustrate the algorithm of fuzzy minimal spanning tree in three different cases, namely, the indifference weighting, the optimistic weighting and the pessimistic weighting. When the structure of the fluid network remains the same and different kinds of uncertainties are considered for simu- lation and analysis of fluid pipeline networks, with appropriate modification, conventional algorithms of graph theory can be utilized to get fuzzy minimal spanning tree, including fuzzy resistance and OERI of three different weighting functions.