模糊元图及其特性分析

模糊图已被广泛地应用于系统的分析与建模。然而现有的结构不适合于分析元素集之间的有向模糊关系。文中讨论了一种新的模糊图论结论－－模糊元图，它描述的是集合而非单个元素之间的有向关系，具有很强的图形化描述功能和形式化分析能力。文中着重分析了模糊元图的特性，尤其是其邻近矩阵的特性，这是模糊元图研究与应用的基础，模糊元图在系统建模和模糊规则管理方面有着广阔的应用前景。

FUZZY METAGRAPHS AND ANALYSIS OF THEIR PROPERTIES

Fuzzy graphs are widely applied in the modeling and analysis of systems. However, existing fuzzy graph-theoretic constructs are unsuitable for the analysis of the directed relationships between sets of elements. In this paper, a new fuzzy graph, the fuzzy metagraph, is discussed, which describes the relationships between sets of fuzzy elements, but not single fuzzy element, and offers some distinct advantages both for graphical visualization of systems as well as for formal analysis of system structure. The paper emphasizes on analyzing the properties of the fuzzy metagraph, especially the properties of its adjacency matrix, which are the basis of researches and applications of fuzzy metagraphs. Fuzzy metagraphs have wide application prospect in fuzzy rule management and system modeling.