Competition graphs with complex intuitionistic fuzzy information

A complex intuitionistic fuzzy set (CIFS) has an ability to represent the problems with intuitionistic uncertainty and periodicity, simultaneously. In this paper, we present a new framework for handling complex intuitionistic fuzzy information by combining the CIFSs with competition graphs. We first introduce the concept of complex intuitionistic fuzzy competition graphs along with its two worthwhile extensions, namely, complex intuitionistic fuzzy k-competition and complex intuitionistic fuzzy p-competition graphs. Further, we present complex intuitionistic fuzzy neighborhood graphs and m-step complex intuitionistic fuzzy competition graphs with some of their remarkable results. We also describe an application of complex intuitionistic fuzzy competition graphs along with an algorithm which finds the competition among the applicants competing for the particular jobs possessing the two-dimensional information. Moreover, we provide a comparison analysis of proposed competition graphs with existing graphs to find the validity and superiority of proposed competition graphs.