The diagram kind of a graph is used to show accumulated data. Graphs can be utilized for a variety of purposes because this data can be either quantitative or qualitative. Graphs can be used to model different relationships and processes in physical, biological, and social media marketing systems, and in finding directions on a map. A graph with properties attached to its nodes and edges that emphasize its applicability to real-world systems is sometimes called a network. The idea of fuzzy sets has developed in numerous ways and across many areas since its establishment in 1965. Applications of this theory can be found in numerous fields for instance in recognition of patterns, management science, AI, computer science, medicine, also in control engineering. The progress of mathematics has reached a very high level and continues now. While classical graph theory is widely applied in several domains, there are instances where its outcomes can be subject to uncertainty. In order to address this challenge, the utilization of the fuzzy theory of graphs is adopted, as it offers more accurate outcomes. There is a lack of a parameterization tool in fuzzy graph theory, as a consequence Molodtsov introduced soft set theory, which is a rather recent way to talk about ambiguity and vagueness. It is becoming more and more popular among scholars and is a novel approach to uncertainty and ambiguity simulation. The concept of soft graphs offers a parameterized perspective on graphs. In this article, we defined some familiar graph families in a fuzzy soft (FS) environment and by calculating their degrees, derived important results for two versions of Sombor numbers. In the end, we discussed an application of calculated results and by comparison, checked the efficiency of Sombor numbers in a FS framework.

中文翻译：

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模糊软图的拓扑数及其应用

图表的图表类型用于显示累积的数据。图表可用于多种目的，因为这些数据可以是定量的，也可以是定性的。图表可用于对物理、生物和社交媒体营销系统中的不同关系和过程进行建模，以及在地图上寻找方向。具有附加到其节点和边的属性的图有时被称为网络，这些属性强调其对现实世界系统的适用性。自 1965 年提出以来，模糊集的概念在许多领域以多种方式得到发展。该理论的应用可以在许多领域找到，例如模式识别、管理科学、人工智能、计算机科学、医学以及控制工程。数学的进步已经达到了很高的水平并且现在仍在继续。虽然经典图论广泛应用于多个领域，但在某些情况下其结果可能会受到不确定性的影响。为了应对这一挑战，采用了图的模糊理论，因为它提供了更准确的结果。模糊图论中缺乏参数化工具，因此莫洛佐夫引入了软集理论，这是讨论模糊性和模糊性的一种相当新的方法。它越来越受到学者的欢迎，是一种不确定性和模糊性模拟的新颖方法。软图的概念提供了图的参数化视角。在本文中，我们在模糊软 (FS) 环境中定义了一些熟悉的图族，并通过计算它们的度数，得出了两个版本的 Sombor 数的重要结果。最后，我们讨论了计算结果的应用，并通过比较检查了 FS 框架中 Sombor 数的效率。