In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternativeshas been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

中文翻译：

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选址问题中图片模糊图的拉普拉斯能量研究

在目前的工作中，已经引入了图片模糊图/有向图的邻接矩阵、能量和拉普拉斯能量及其上下界。此外，在决策的选择问题中，利用图片模糊图及其能量/拉普拉斯能量，提出了一种对可用备选方案进行排序的方法。为震撼示范所引入方法的实施，水电站选址任务已作为应用程序进行。与直觉模糊和毕达哥拉斯模糊信息相比，还研究了所介绍方法的独创性、比较性评论、优势特征和局限性。