In the literature of application fields of science and technology, various matrix systems involving Lyapunov, Sylvester, & Stein matrix equations have been investigated and paid attention by different researchers in the last decades. In view of this, various algebraic operations and properties like addition, multiplication, associative, distributive, and commutative have been studied in the case of the complex fuzzy matrix (CFM). In addition to this, a new similarity measure has also been proposed for CFMs along with a detailed explanatory numerical example. The proposed modification and extension significantly contribute in order to model the uncertainty & inexactness a little more accurately. Further, an application in the area of identification of reference signals has been described with the help of the CFM and operations.