Today, fuzzy graphs (FGs) have a variety of applications in other 2elds of study, including medicine, engineering, and psychology, and for this reason, many researchers around the world are trying to identify their properties and use them in computer sciences as well as 2nding the smallest problem in a network. 'e concept of a Cayley fuzzy graph has become a standard part of the toolkit used to investigate and describe groups. Also, Cayley fuzzy graphs are good models for interconnection networks, and they are useful in semigroup theory for establishing which elements are - and R related. 'e previous de2nition limitations in the FGs have directed us to o3er a new classi2cation in terms of Cayley fuzzy graphs. So, in this paper, two new de2nitions of Cayley fuzzy graphs (CFGs) and pseudo-Cayley fuzzy graphs (PCFGs) are discussed and their rough approximations are studied. Also, some properties of fuzzy rough sets (FRSs) in CFGs and PCFGs have been investigated. Finally, we presented the determination of the most e3ective person in the Water and Sewerage Organization and the importance of using refereeing facilities in football matches between club teams, by using CFG in the presented applications.
