The purpose of this article is to present a novel idea of complex Pythagorean fuzzy threshold graphs \((\mathcal {CPFTG}_{s})\). We introduce the relation between vertex cardinality and threshold values of a \(\mathcal {CPFTG}\). We propose that \(\mathcal {CPFTG}_{s}\) are free from alternating \(4-cycle\) and these graphs can be built up repeatedly adding an isolated or a dominating vertex. We present that the crisp graph of \(\mathcal {CPFTG}\) is a split graph \((\mathcal {SG})\). Further, the threshold dimension and threshold partition number of \(\mathcal {CPFG}_{s}\) is defined. Some basic results on threshold dimension and threshold partition number also have been discussed. Finally, an application is presented on this developed concept. Due to the wide range of complex Pythagorean fuzzy sets \((\mathcal {CPFS}_{s})\), it is obvious that \(\mathcal {CPFTG}_{s}\) are more helpful and beneficial in modeling a problem as compared to complex fuzzy threshold graphs \((\mathcal {CFTG}_{s})\) and complex intuitionistic fuzzy threshold graphs \((\mathcal {CIFTG}_{s})\).

本文的目的是提出复杂勾股模糊阈值图\((\mathcal {CPFTG}_{s})\) 的新思想。我们介绍了\(\mathcal {CPFTG}\) 的顶点基数和阈值之间的关系。我们建议\(\mathcal {CPFTG}_{s}\)不受交替\(4-cycle\) 的影响，并且这些图可以通过添加一个孤立的或主导的顶点来重复构建。我们提出\(\mathcal {CPFTG}\)的清晰图是一个分裂图\((\mathcal {SG})\)。进一步，\(\mathcal {CPFG}_{s}\)的阈值维度和阈值分区数被定义为。还讨论了阈值维数和阈值分区数的一些基本结果。最后，介绍了一个关于这个开发概念的应用程序。由于复杂的勾股模糊集\((\mathcal {CPFS}_{s})\) 的范围很广，很明显\(\mathcal {CPFTG}_{s}\)对建模更有帮助和好处与复杂的模糊阈值图\((\mathcal {CFTG}_{s})\)和复杂的直觉模糊阈值图\((\mathcal {CIFTG}_{s})\) 相比，这是一个问题。