A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

复杂模糊集（CFS）是模糊集的显着概括，其中隶属函数被限制为从复杂平面中的单位圆获取值。CFS是一种有效的模型，由于存在相位项，因此可以更全面，更逻辑地处理人类判断的不确定性。在本文中，我们介绍了复杂模糊环境下竞争图的概念。此外，我们提出了复杂的模糊k-竞争图和p-竞争复杂的模糊图。此外，我们考虑m阶复杂模糊竞争图，复杂模糊邻域图（CFNG），复杂模糊经济竞争图（CFECG）和m有趣特性的多步复杂模糊经济竞争图。另外，我们描述了我们提出的模型在生态系统中的应用。我们还提供了建议竞争图与现有图的比较。