Abstract
This manuscript aims to analyze the well-known and massive idea of competition graph (CG) in the presence of a new and dominant technique of complex q-rung orthopair fuzzy (CQROF) setting. The mathematical form of the CQROF setting is more flexible and massive consistent for demonstrating the beneficial option from the collection of objectives during the decision-making process. Additionally, the major concept of in-neighbourhood and out-neighbourhood using CQROF diagraph (CQROFDG) are also invented to enhance the quality of the diagnosed approach. The fundamental theory of CQROF k-competition, CQROF p-competition, CQROF neighbourhood and m-step CQROF neighbourhood graphs are also explored. In the availability of the above-described theories, the basic and significant results for the presented work are obtained to show the compatibility and worth of the invented approaches. To show the practicality of the developed approach, we try to verify the proposed work with the help of various examples. Further, to describe the validity and practicality of the invented work, we diagnosed an application using presented approaches based on the CQROF setting is to enhance the major weakness of the existing approaches. Finally, in the availability of the invented ideas, we discussed the sensitivity analysis of the described approaches.