Abstract The authors (Mathew and Sunitha (2010) [9] ) introduced the concept of fuzzy arc cuts for improving the definition of the so-called cut-sets proposed by Yeh and Bang, both generalizing edge cuts from classic graph theory to the fuzzy settings. They argued that non-strong edges need not be considered in a fuzzy arc cut as such edges would not change the strength of connectedness between any vertices. However, we give a counterexample in the paper, which illustrates that this viewpoint may contain some flaws. Based on this observation, a more general definition of fuzzy arc cuts (called fuzzy edge cuts) is given. Moreover, we define fuzzy edge connectivity with two parameters, this definition allows us to talk about edge connectivity more precisely. The concepts of fuzzy local edge cuts and fuzzy local edge connectivity are also introduced. We investigate the relations between fuzzy edge cuts and fuzzy local edge cuts. A characterization for the weight of a minimal fuzzy local edge cut is obtained. Finally, we provide some algorithms to compute fuzzy edge connectivity and fuzzy local edge connectivity of special graphs. Besides, applications of two connectivity parameters in communication networks are presented.

中文翻译：

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模糊边缘连通性和模糊局部边缘连通性及其在通信网络中的应用

摘要 作者 (Mathew and Sunitha (2010) [9] ) 引入了模糊弧切割的概念，以改进 Yeh 和 Bang 提出的所谓割集的定义，两者都将边缘割从经典图论推广到模糊设置。他们认为在模糊弧切割中不需要考虑非强边，因为这样的边不会改变任何顶点之间的连接强度。但是，我们在论文中给出了一个反例，说明这个观点可能存在一些缺陷。基于这一观察，给出了模糊弧切割（称为模糊边缘切割）的更一般定义。此外，我们用两个参数定义了模糊边缘连通性，这个定义使我们能够更精确地讨论边缘连通性。还介绍了模糊局部边缘切割和模糊局部边缘连通性的概念。我们研究了模糊边缘切割和模糊局部边缘切割之间的关系。获得了最小模糊局部边缘切割的权重特征。最后，我们提供了一些算法来计算特殊图的模糊边连通性和模糊局部边连通性。此外，还介绍了两个连通性参数在通信网络中的应用。