Picture fuzzy graphs are an extension of intuitionistic fuzzy graphs. Balanced picture fuzzy graph is a special type of picture fuzzy graph (PFG). In this study, the definition and important properties of PFG like, average PFG, balanced PFG, size, order, density of a PFG, isomorphism, the direct product of two PFG, etc have been studied. The necessary and sufficient conditions for balanced picture fuzzy graphs have also been studied in this article. Beside this, we proposed an algorithm to test whether a PFG is balanced or not. The proof of correctness and an illustration of the proposed algorithm is presented in this article. Lastly, an application of balanced PFG to business alliance is presented.

图片模糊图是直觉模糊图的扩展。平衡图片模糊图是一种特殊类型的图片模糊图（PFG）。在本研究中，研究了PFG的定义和重要性质，如平均PFG、平衡PFG、尺寸、阶数、一个PFG 的密度、同构性、两个PFG的直积等。本文还研究了平衡图像模糊图的充要条件。除此之外，我们提出了一种算法来测试一个PFG是否平衡。本文提供了正确性证明和所提出算法的说明。最后，介绍了平衡PFG在商业联盟中的应用。