A q-rung orthopair fuzzy set (q-ROFS) is more practical and powerful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) to model uncertainty in various decision-making problems. In this research article, we introduce the notion of q-rung orthopair fuzzy Hamacher graphs (q-ROFHGs).We utilize the Hamacher operators because they are flexible and parameterized in decision making. We determine the energy of q-ROFHGs as well as the energy of splitting and shadow q-ROFHGs. In addition, we propose the Randić energy of q-ROFHG and its some substantial results. Further, we present the idea of q-rung orthopair fuzzy Hamacher digraphs (q-ROFHDGs). We solve a decision-making numerical example related to the selection of best housing society for investment by calculating the energy and Randić energy of q-ROFHDGs and an algorithm to exhibit the applicability of the presented concepts in decision making. Finally, we present the conclusion.

中文翻译：

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Hamacher算子下的q-Rung正交对模糊图

q阶邻对模糊集（q-ROFS）比直觉模糊集（IFS）和勾股模糊集（PFS）更实用，功能更强大，可以对各种决策问题中的不确定性进行建模。在本文中，我们介绍了q阶正交对模糊Hamacher图（q-ROFHGs）的概念。我们利用Hamacher算子是因为它们在决策过程中具有灵活性和参数化性。我们确定q-ROFHGs的能量以及分裂和影子q-ROFHGs的能量。此外，我们提出了q-ROFHG的兰迪奇能量及其一些实质性结果。此外，我们提出了q级正交对对模糊Hamacher有向图（q-ROFHDGs）的思想。我们通过计算q-ROFHDGs的能量和Randić能量以及一种算法来展示与选择最佳住房社会有关的决策数值示例，并通过算法展示出所提出的概念在决策中的适用性。最后，我们提出结论。