In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose analgorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.

中文翻译：

---

模糊度量：一种解决网络附加信息的社区检测问题的解决方案

在这项工作中，我们介绍了与模糊测度相关的加权图的概念。有一组有限的元素之间存在亲和力模糊关系，我们根据个体之间的亲和力模糊关系提出了一个组的定义。然后，我们提出基于Louvain方法的算法，以独立于图的附加信息处理社区检测问题。我们还提供了一种特殊的方法来解决扩展模糊图上的社区检测问题。最后，我们通过在几个基准模型中计算出的一些详细的计算测试来测试我们提案的性能。