Relation among companies.

Recent developments in the theory of fuzzy graphs have led to many extensions for modeling real-world problems involving uncertainty. Among these, competition graphs are crucial for representing competitive and ecological systems. In this study, the notion of bipolar picture fuzzy competition graphs, along with several generalizations including bipolar picture fuzzy k-competition graphs, p-competition graphs, and m-competition graphs are introduced. Several characteristics of these newly established graphs are investigated. We also explore their structural properties and apply the models to real-world competitive scenarios using computational frameworks. A comparative study is conducted to demonstrate the improved efficiency of the proposed models over existing approaches.模糊图（fuzzy graphs）理论的新近发展，催生了诸多可用于建模各类含不确定性现实问题的扩展形式。其中，竞争图（competition graphs）在表征竞争系统与生态系统方面具有关键作用。本研究提出了双极图片模糊竞争图（bipolar picture fuzzy competition graphs）的概念，并引入其若干推广形式，包括双极图片模糊k-竞争图（bipolar picture fuzzy k-competition graphs）、p-竞争图（p-competition graphs）以及m-竞争图（m-competition graphs）。研究对上述新构建的图类的多项特征展开了探究，同时分析了其结构性质，并借助计算框架将所提模型应用于现实竞争场景中。此外，本研究开展了对比实验，以证明所提模型相较于现有方法具备更优异的运行效率。