In recent years, the concept of domination has been the backbone of research activities in graph theory. The application of graphic domination has become widespread in different areas to solve human-life issues, including social media theories, radio channels, commuter train transportation, earth measurement, internet transportation systems, and pharmacy. The purpose of this paper was to generalize the idea of bondage set (BS) and non-bondage set (NBS), bondage number $\alpha \left(G\right)$, and non-bondage number ${\alpha }_k\left(G\right)$, respectively, in the intuitionistic fuzzy graph (IFG). The BS is based on a strong arc (SA) in the fuzzy graph (FG). In this research, a new definition of SA in connection with the strength of connectivity in IFGs was applied. Additionally, the BS, $\alpha \left(G\right)$, NBS, and ${\alpha }_k\left(G\right)$ concepts were presented in IFGs. Three different examples were described to show the informative development procedure by applying the idea to IFGs. Considering the examples, some results were developed. Also, the applications were utilized in water supply systems. The present study was conducted to make daily life more useful and productive.

中文翻译：

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直觉模糊图的新概念及其在供水系统中的应用

近年来，控制的概念已成为图论研究活动的骨干。图形化控制的应用已广泛应用于解决人类生活问题的不同领域，包括社交媒体理论，广播频道，通勤火车运输，地球测量，互联网运输系统和药房。本文的目的是概括束缚集（BS）和非束缚集（NBS）的概念，束缚数$\alpha （G）$和非绑定数 ${\alpha }_{ķ}（G）$分别在直觉模糊图（IFG）中。BS基于模糊图（FG）中的强弧（SA）。在这项研究中，应用了与IFG中的连接强度相关的SA的新定义。此外，BS$\alpha （G）$，NBS和 ${\alpha }_{ķ}（G）$IFG中提出了一些概念。描述了三个不同的示例，以通过将该思想应用于IFG来展示信息开发过程。考虑这些示例，得出了一些结果。此外，这些应用还用于供水系统中。进行本研究是为了使日常生活更加有用和多产。