区间值模糊图和模糊拟阵

Interval-Valued Fuzzy Graphs and Fuzzy Matroids

图与拟阵有着密切的联系。本文研究区间值模糊图与模糊拟阵之间的关系。对于任意一个区间值模糊图,通过区间排序诱导出一个模糊图。由截模糊图得到一系列分明图,又因为每个分明图都可以得到一个圈拟阵,从而可获得拟阵序列。最后由拟阵序列构造出一个模糊拟阵。最后指出区间值模糊图和模糊拟阵之间不存在一一对应关系。

Graphs and matroids have a close relationship.In this paper,we study the relation between interval valued fuzzy graph and fuzzy matroid.For any interval valued fuzzy graph,it can induce a fuzzy graph by interval ordering.And then a sequence of crisp graphs can be obtained by cuts of the fuzzy graph.Since a crisp graph can induce a cycle matroid,a sequence of matroids will be constructed.We finally construct a fuzzy matroid from the induced sequence of matroids.Finally,we point out that there is no one-to-one correspondence between interval-valued fuzzy graphs and fuzzy matroids.