区间值模糊图的图塔分解与表示定理

The Graph Tower Decomposition and Representation Theorems of the Interval-valued Fuzzy Graph

利用偏序集的同构关系研究区间值模糊图的图塔分解与表示.借助于所定义的[0,1]上区间集的划分,研究区间值模糊图的图集表示,证明[0,1]上区间集的划分与其对应的图集具有相同的序结构.同时,给出区间值模糊图的图塔分解及运算法则,建立区间值模糊图塔与区间值模糊图的同构关系.作为模糊图运算及其应用的基础性研究,得到了图集与区间值模糊图的转换定理.

We discuss the graph tower decomposition and representation theorems of the interval-valued fuzzy graph by using homogeneous transformation of posets.Furthermore,the subgraph representation of the interval-valued fuzzy graph is investigated by means of the partition of the class of sub-intervals on[0,1]proposed in this paper,it shows that an interval-valued fuzzy graph and its corresponding partition of the class of sub-intervals on[0,1]have the same ordering structure.In addition,the graph tower decomposition and the operation of the interval-valued fuzzy graph are obtained,and it is shown that the interval-valued fuzzy graph tower is isomorphic with the interval-valued fuzzy graph.As a fundamental research of the operation and its applications of the interval-valued fuzzy graph,the transformation theorem of the class of graphs and the interval-valued fuzzy graph is also given.