In this study, the embedding of picture fuzzy graphs on the surface of spheres is introduced. The picture fuzzy genus graph with its genus value and strong (weak) picture fuzzy genus graphs are defined. Some important properties of picture fuzzy genus graphs are discussed. A relation between genus value and degree of planarity of picture fuzzy graph is established. The isomorphism properties of picture fuzzy genus graphs are studied. The Euler polyhedral equation in terms of genus value is established here. Finally, two real-life applications of picture fuzzy genus graph in traffic problem on road network and electronic circuit design on planar sheet are exhibited.

中文翻译：

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图片模糊环境下图形的属及其应用

在这项研究中，介绍了在球表面上嵌入图片模糊图的方法。定义了图像模糊属图及其属值和强（弱）图像模糊属图。讨论了图像模糊属图的一些重要性质。建立属值与图像模糊图的平面度之间的关系。研究了图片模糊属图的同构性质。在这里建立了基于属值的欧拉多面体方程。最后，展示了图像模糊类图在道路交通问题和平面电子电路设计中的两种实际应用。